Papers

With Ilya Spitkovsky in Bordeaux
 

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220. Albrecht Böttcher, Barry Simon, and Ilya Spitkovsky:
Similarity between two projections.
arXiv:1705.08937 [math FA] (2017).

219.
A. Böttcher, S. Eisenbarth, L. Fukshansky, S. R. Garcia, and H. Maharaj:
Spherical 2-designs and lattices from Abelian groups.
Discrete & Computational Geometry, online first (2017).

218.

A. Böttcher and L. Fukshansky:
Addendum to "Lattices from equiangular tight frames".
Linear Algebra Appl. 531, 592-601 (2017).

217.
A. Böttcher and C. Rebs:
On the constants in Markov inequalities for the Laplace operator on polynomials with
the Laguerre norm.

Asymptotic Analysis 101, 227-239 (2017).

216.
A. Böttcher:
The Duduchava-Roch formula.
Operator Theory:  Adv. and Appl. 258, 1-19 (2017).

215.

A. Böttcher,  L. Fukshansky, S. R. Garcia, and H. Maharaj:
Lattices from Abelian groups.
Oberwolfach Reports 13, 121-124 (2016).

214.
A. Böttcher and F.-O. Speck:
On the symmetrization of general Wiener-Hopf operators.
J. Operator Theory 76, 335-349 (2016).

213.

A. Böttcher,  L. Fukshansky, S. R. Garcia, H. Maharaj, and D. Needell:
Lattices from equiangular tight frames.
Linear Algebra Appl. 510, 395-420 (2016).

212.
A. Böttcher, H. Langenau, and H. Widom:
Schatten class integral operators occurring in Markov-type inequalities.
Operator Theory:  Adv. and Appl. 255, 91-104 (2016).

211.
M. Bogoya, A. Böttcher, and E.A. Maximenko:
From convergence in distribution to uniform convergence.
Boletín de la Sociedad Matemática Mexicana 22, 695-710 (2016).

210.
A. Böttcher:
The part of my path I walked together with Sergei Grudsky.
Boletín de la Sociedad Matemática Mexicana 22, 309-327 (2016).

209
A. Böttcher and F. Kittaneh:
The limit of the zero set of polynomials of the Fibonacci type.
Journal of
  Number Theory 163, 89-100 (2016).

208.

M. Bogoya, A. Böttcher,  S. Grudsky, and E.A. Maximenko:
Eigenvectors of Hermitian Toeplitz matrices with smooth simple-loop symbols.
Linear Algebra Appl. 493, 606-637 (2016).

Here is an
interactive visualization of eigenvalues and eigenvectors of Kac–Murdock–Szegő Toeplitz matrices.

207.
Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, and Hiren Maharaj:
Lattices from Hermitian function fields.
Journal of Algebra 447, 560-579 (2016).

206.
Albrecht Böttcher, Danny Kowerko, and Roland K. O. Sigel:
Explicit analytic equations for multimolecular thermal melting curves.
Biophysical Chemistry 202, 32-39 (2015).

205.
M. Bogoya, A. Böttcher,  S. Grudsky, and E.A. Maximenko:
Maximum norm versions of the Szegö and Avram-Parter theorems for Toeplitz matrices.
J. Approx. Theory 196, 79--100 (2015).

204.
Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, and Hiren Maharaj:
On lattices generated by finite Abelian groups.
SIAM J. Discrete Math. 29, 382--404 (2015).

203.
Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, and Hiren Maharaj:
Toeplitz determinants with perturbations in the corners.
J. Funct. Analysis 268, 171-193 (2015).

202.
M. Bogoya, A. Böttcher,  S. Grudsky, and E.A. Maximenko:
Eigenvalues of Hermitian Toeplitz matrices with smooth simple-loop symbols.
J. Math. Analysis Appl. 422, 1308-1334 (2015).

201.
A. Böttcher and M. Halwass:
Canonical Wiener-Hopf and spectral factorization of large-degree matrix polynomials.
Proceedings in Applied Mathematics and Mechanics (PAMM) 14, 817 – 818 (2014).

200.
A. Böttcher:
On Hurwitz stable polynomials with integer coefficients.
Computational Methods and Function Theory 14, 139-156 (2014).

199.
A. Böttcher:
Borodin-Okounkov and Szegö for Toeplitz operators on model spaces.
Integral Equations and Operator Theory 78, 407-414 (2014).

198.
A. Böttcher and M. Halwass:
A Newton method for canonical Wiener-Hopf and spectral factorization of matrix polynomials.
Electronic Journal of Linear Algebra (ELA) 26, 873-897 (2013).


197.
A. Böttcher and I. Spitkovsky:
Special types of matrices.
Chapter 22 of the Handbook of Linear Algebra, 2nd edition, edited by Leslie Hogben,
Chapman & Hall/CRC, Boca Raton 2013.

196.
A. Böttcher:
Best constants for Markov type inequalities in Hilbert space norms.
In: Recent Trends in  Analysis, Proceedings of the Conference in Honor of Nikolai Nikolski,
Bordeaux 2011, pp. 73-83, Theta, Bucharest 2013.

195.
A. Böttcher:
An operator theoretic approach to the brickwork Ising model with second-neighbor interactions.
Linear Algebra Appl. 439, 675-685 (2013).


194.
A. Böttcher and I. Spitkovsky:
Classification of the finite-dimensional algebras generated by two tightly coupled idempotents.
Linear Algebra Appl. 439, 538-551 (2013).


193.
A. Böttcher and M. Halwass:
Wiener-Hopf and spectral factorization of real polynomials by Newton's method.
Linear Algebra Appl. 438, 4760-4805 (2013).


192.
A. Böttcher and I. Spitkovsky:
The factorization problem: some known results and open questions.
Operator Theory:  Adv. and Appl. 229, 101-122 (2013).

191.
A. Böttcher and Antti Perälä:
The index formula of Douglas for block Toeplitz operators on the Bergman space of the ball.
Operator Theory:  Adv. and Appl. 228, 39-55 (2013).

190.
Albrecht Böttcher and Albrecht Pietsch:
Orthogonal and skew-symmetric operators in real Hilbert space.
Integral Equations and Operator Theory 74, 497-511  (2012).

189.
A. Böttcher, S. Grudsky, and A. Iserles:
The Fox-Li operator as a test and a spur for Wiener-Hopf theory.
In: Essays in Mathematics and Its Applications, in Honor of Stephen Smale's 80th Birthday,
pp.
37-48, Springer-Verlag, Heidelberg 2012.

188.
A. Böttcher and I. Spitkovsky:
Group inversion in certain finite-dimensional algebras generated by two idempotents.
Indagationes Mathematicae 23, 715-732 (2012).

187.
M. Bogoya, A. Böttcher, and S. Grudsky:
Eigenvalues of Hermitian Toeplitz matrices with polynomially increasing entries.
Journal of  Spectral Theory 2, 267-292 (2012).

186.
M. Bogoya, A. Böttcher, S. Grudsky, and E. A. Maksimenko:
Eigenvectors of  Hessenberg Toeplitz matrices and a problem by Dai, Geary, and Kadanoff.
Linear Algebra Appl. 436, 3480-3492 (2012).

185.
M. Bogoya, A. Böttcher, and S. Grudsky:
Asymptotics of individual eigenvalues of a class of large Hessenberg Toeplitz matrices.
Operator Theory: Adv. and Appl. 220, 77-95 (2012).

184.
A. Böttcher, S. Grudsky, D. Huybrechs, and A. Iserles:
First-order trace formulae for the iterates of the Fox-Li operator.
Operator Theory: Adv. and Appl. 218, 207-224 (2012).

183.
A. Böttcher and I. Spitkovsky:
On certain finite-dimensional algebras generated by two idempotents.
Linear Algebra Appl. 435, 1823-1836 (2011).

182.
A. Böttcher, S. Grudsky, and A. Iserles:
Spectral theory of large Wiener-Hopf operators with complex-symmetric kernels and rational symbols.
Math. Proc. Cambridge Phil. Soc. 151, 161-191 (2011).

181.
A. Böttcher:
The algebraic Riccati equation with Toeplitz matrices as coefficients.
Electronic
Journal of Linear Algebra (ELA) 22, 348-362 (2011).

180.
A. Böttcher and P. Dörfler:
Inequalities of the Markov type for partial derivatives of polynomials in several variables.
J. Integral Equations Appl. 23, 1-37 (2011).

179.
A. Böttcher,  S. Grudsky, and  R. M. Porter:
European double-barrier options with a compound Poisson component.
In: Progress in Economics Research, Vol. 18 (A. Tavidze, ed.), pp. 315-331, 
Nova Science Publishers, Huntington, NY, 2011.


178.
A. Böttcher and P. Dörfler:
On the best constants in Markov-type inequalities involving Gegenbauer norms with different weights.
Operators and Matrices 5, 261-272 (2011).

177.
M. Bogoya, A. Böttcher, S. Grudsky, and E. A. Maksimenko:

Eigenvalues of Hessenberg Toeplitz matrices generated by symbols with several singularities.
Commun. Math. Analysis, Conf. 03, 23-41 (2011).

176.
A. Böttcher, H. Brunner, A. Iserles, and
S. P. Nørsett:
On the singular values and eigenvalues of the Fox-Li and related operators.
New York J. Math. 16, 539-561 (2010).

175.
A. Böttcher and P. Dörfler:
On the best constants in Markov-type inequalities involving Laguerre norms with different weights.
Monatshefte f. Math. 161, 357-367 (2010).


174.
A. Böttcher, S. Grudsky, and E. A. Maksimenko:
On the structure of the eigenvectors of large Hermitian Toeplitz band matrices.
Operator Theory: Adv. and Appl. 210, 15-36 (2010).


173.
A. Böttcher and S. Grudsky:
Variable-coefficient Toeplitz matrices with  symbols beyond the Wiener algebra.
Operator Theory: Adv. and Appl. 199, 192-202 (2010).

172.
A. Böttcher, S. Grudsky, and E. A. Maksimenko:
Inside the eigenvalues of certain Hermitian Toeplitz band matrices.
J. Comput. Appl. Math. 233, 2245-2264 (2010).

171.
A. Böttcher and I. Spitkovsky:
A gentle guide to the basics of two projections theory.
Linear Algebra Appl. 432, 1412-1459 (2010).

170.
A. Böttcher and P. Dörfler:
Weighted Markov-type inequalities, norms of Volterra operators, and zeros of Bessel functions.
Math. Nachr. 283, 40-57 (2010).

169.
A. Böttcher, S. Grudsky, and E. A. Maksimenko:
On the asymptotics of all eigenvalues of Hermitian Toeplitz band matrices (Russian).
Dokl. Akad. Nauk 428, 153-156 (2009);
Engl. transl. in Doklady Math. 80,  662-664 (2009).

168.
A. Böttcher and I. Spitkovsky:

Drazin inversion in the von Neumann algebra generated by two orthogonal projections.
J. Math. Analysis Appl.
358, 403-409 (2009).

167.
A. Böttcher, S. Kunis, and D. Potts:
Probabilistic spherical Marcinkiewicz-Zygmund inequalities.
J. Approx. Theory 157, 113-126 (2009).

166.
A. Böttcher,  S. Grudsky,
E. A. Maksimenko, and J. Unterberger:
The first order asymptotics of the extreme eigenvectors of certain Hermitian Toeplitz matrices.
Integral Equations and Operator Theory 63, 165-180 (2009).

165.
A. Böttcher and P. Dörfler:
On the best constants in inequalities of the Markov and Wirtinger types for polynomials on the half-line.
Linear Algebra Appl. 430, 1057-1069 (2009).

164.
A. Böttcher and M. Lindner:
Pseudospectrum.
Scholarpedia 3(3):2680 (2008).

163.
A. Böttcher, S. Grudsky, and J. Unterberger:
Asymptotic pseudomodes of Toeplitz matrices.
Operators and Matrices 2, 525-541 (2008).

162.
A. Böttcher and D. Wenzel:
The Frobenius norm and the commutator.
Linear Algebra Appl. 429, 1864-1885 (2008).


161.
A. Böttcher:
Linear and one-dimensional.
In: Israel Gohberg and Friends (H. Bart, T. Hempfling, M. A. Kaashoek,
editors), pp. 291-293, Birkhäuser Verlag, Basel 2008.

160.
A. Böttcher and D. Wenzel:
Rigorous stochastic bounds for the error in large covariance matrices.
Math. Methods Appl. Sci. 31, 1209-1220 (2008).

159.
A. Böttcher:
Orthogonal symmetric Toeplitz matrices.
Complex Analysis and Operator Theory 2, 285-298 (2008).


158.
A. Böttcher, S. Grudsky, and E. A. Maksimenko:
Pushing the envelope of the test functions in the Szegö and Avram-Parter theorems.
Linear Algebra Appl. 429, 346-366 (2008).

157.
A. Böttcher, S. Grudsky, and E. A. Maksimenko:
The Szegö and Avram-Parter theorems for general test functions.
C. R. Math. Acad. Sci. Paris 346, 749-752 (2008).

156.
A. Böttcher, S. Grudsky, and M. Schwartz:
Some problems concerning the test functions in the Szegö and Avram-Parter theorems.
Operator Theory:  Adv. and Appl. 187, 81-93 (2008).

155.
A. Böttcher and S. Grudsky:
Uniform boundedness of Toeplitz matrices with variable coefficients.
Integral Equations Operator Theory 60, 313-328 (2008).

154.
A. Böttcher, A. Karlovich, and B. Silbermann:
Generalized Krein algebras and asymptotics of Toeplitz determinants.
Methods of Functional Analysis and Topology 13,  236-261 (2007).

153.
A. Böttcher and J. Virtanen:
Norms of Toeplitz matrices with Fisher-Hartwig symbols.
SIAM J. Matrix Analysis Appl. 29, 660-671 (2007).

152.
A. Böttcher and D. Potts:
Probability against condition number and sampling of multivariate trigonometric random polynomials.
Electronic Transactions on Numerical Analysis (ETNA) 26, 178-189 (2007) .

151.
A. Böttcher, Jesús Gutiérrez-Gutiérrez, and Pedro M. Crespo:
Mass concentration in quasicommutators of Toeplitz matrices.
J. Comput. Appl. Math. 205, 129-148 (2007).


150.
A. Böttcher, D. Potts, and D. Wenzel:
A probability argument in favor of ignoring small singular values.
Operators and Matrices 1, 31-43 (2007).

149.
Jesús Gutiérrez-Gutiérrez,  Pedro M. Crespo, and A. Böttcher:
Functions of banded Hermitian block Toeplitz matrices in signal processing.
Linear Algebra Appl. 422, 788-807 (2007).


148.
A. Böttcher and D. Wenzel:

On the verification of linear equations and the identification of the Toeplitz-plus-Hankel structure.
Operator Theory: Adv. and Appl. 170,  43-51 (2007).

147.
A. Böttcher and H. Widom:
Szegö via Jacobi.
Linear Algebra Appl. 419, 656-667 (2006).

146.
A. Böttcher:
Schatten norms of Toeplitz matrices with Fisher-Hartwig singularities.
Electronic Journal of Linear Algebra (ELA) 15, 251-259 (2006).

145.
A. Böttcher and H. Widom:
On the eigenvalues of certain canonical higher-order ordinary differential operators.
J. Math. Analysis Appl. 322, 990-1000 (2006).

144.
A. Böttcher and H. Widom:
From Toeplitz eigenvalues through Green's  kernels to higher-order Wirtinger-Sobolev inequalities.
Operator Theory:  Adv. and Appl. 171, 73-87 (2006).

143.
A. Böttcher:
Review of "Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators"
by L. N. Trefethen and M. Embree.

Linear Algebra Appl. 416, 1098-1101 (2006).


142.
A. Böttcher, B. Hofmann, U. Tautenhahn, and M. Yamamoto:
Convergence rates for Tikhonov regularization from different kinds of smoothness conditions.
Applicable Analysis 85, 555-578 (2006).


141.
Z. Hurak, A. Böttcher, and M. Sebek:
Minimum distance to the range of a banded lower triangular Toeplitz operator
in l^1 and application in l^1-optimal control.

SIAM J.  Control Optim. 45, 107-122 (2006).

140.
A. Böttcher:
On the problem of testing the structure of a matrix by displacement operations.
SIAM J. Numerical Analysis 44, 41-54 (2006).


139.
A. Böttcher, S. Grudsky, and E. Ramírez de Arellano:
On the asymptotic behavior of the eigenvectors of large banded Toeplitz matrices.
Math. Nachr. 279, 121-129 (2006).

138.
A. Böttcher and H. Widom:
Two elementary derivations of the pure Fisher-Hartwig determinant.
Integral Equations Operator Theory 53, 593-596 (2005).

137.
A. Böttcher and P. Otte:
The first Szegö limit theorem for non-selfadjoint operators in the Følner algebra.
Mathematica Scandinavica 97, 115-126 (2005).

136.
A. Böttcher, I. Gohberg, and B. Silbermann:
Georg Heinig (1947-2005) In Memoriam.
Integral Equations Operator Theory 53, 297-300  (2005).

135.
A. Böttcher and S. Grudsky:

Structured condition numbers of large Toeplitz matrices are rarely better than usual condition numbers.
Numerical Linear Algebra with Applications 12, 95-102 (2005).

134.
A. Böttcher and D. Wenzel:
How big can the commutator of two matrices be and how big is it typically?
Linear Algebra Appl. 403, 216-228 (2005).

133.
Z. Hurak and A. Böttcher:
MIMO l^1-optimal control via block Toeplitz operators.
In: Proceedings of 16th International Symposium on Mathematical Theory of Networks and
Systems (MTNS'04), Katholieke Universiteit Leuven 2004.

132.
A. Böttcher and K. Rost:
Topics in the numerical linear algebra of Toeplitz and Hankel matrices.
GAMM-Mitteilungen 27, 174-188 (2004).

131.
A. Böttcher, S. Grudsky, and E. Ramírez de Arellano:
Approximating inverses of Toeplitz matrices by circulant matrices.
Methods and Applications of Analysis 11, 211-220 (2004).

130.
A. Böttcher:
The constants in the asymptotic formulas by Rambour and Seghier for inverses of Toeplitz matrices.
Integral Equations and Operator Theory 50, 43-55 (2004).

129.
A. Böttcher,  S. Grudsky, and E.
Ramírez de Arellano:
Algebras of Toeplitz operators with oscillating symbols.
Revista Matematica Iberoamericana  20, 647-671 (2004).

128.
A. Böttcher:
Transient behavior of powers and exponentials of large Toeplitz matrices.
Electronic Transactions on Numerical Analysis (ETNA)  18, 1-41 (2004).

127.
A. Böttcher and S. Grudsky:
Asymptotically good pseudomodes for Toeplitz matrices and Wiener-Hopf operators.
Operator Theory: Adv. and Appl. 147, 175-188 (2004).

126.
A. Böttcher and B. Silbermann:

Erhard Meister - friend and colleague.
Operator Theory: Adv. and Appl.
147,  p. 67 (2004).

125.
A. Böttcher and S. Grudsky:

Fejér means and norms of large Toeplitz matrices.
Acta Sci. Math. (Szeged)  69, 889-900 (2003).

124.
A. Böttcher, Yu. I. Karlovich, and I. Spitkovsky:

The C*-algebra of singular integral operators with semi-almost periodic coefficients.
J. Funct. Analysis  204, 445-484 (2003).

123.
A. Böttcher and S. Grudsky:
Toeplitz matrices with slowly growing pseudospectra.
In: Factorization, Singular Operators and Related Problems in Honour
of Georgii Litvinchuk (S. Samko, A. Lebre, A. F. dos Santos, eds.), pp. 43-54,
Kluwer Academic Publishers, Dordrecht 2003.

122.
A. Böttcher and S. Grudsky:
Asymptotic spectra of dense Toeplitz matrices are unstable.
Numerical Algorithms 33, 105-112 (2003).

121.
A. Böttcher and S. Grudsky:
The norm of the product of a large matrix and a random vector.
Electronic Journal of Probability , Vol. 8,  Paper no. 7, pages 1-29 (2003).

120.
A. Böttcher, S. Grudsky, and I. Spitkovsky:
Block Toeplitz operators with frequency-modulated semi-almost periodic symbols.
Int. J.  Math.  Math. Sci. 2003:34, 2157-2176 (2003).

119.
A. Böttcher, M. Embree, and V. I. Sokolov:
The spectra of  large Toeplitz band matrices with a randomly perturbed entry.
Mathematics of  Computation 72, 1329-1348 (2003).

118.
A. Böttcher, S. Grudsky, and I. Spitkovsky:
On the essential spectrum of Toeplitz operators with semi-almost periodic symbols.
Operator Theory: Adv. and Appl. 142, 59-77 (2003).

117.
D. Bini and A. Böttcher:
Polynomial factorization through Toeplitz matrix computations.
Linear Algebra Appl. 366, 25-37 (2003).

116.
A. Böttcher, M. Embree, and V. I. Sokolov:
On large Toeplitz band matrices with an uncertain block.
Linear Algebra Appl. 366, 87-97 (2003).

115.
A. Böttcher, M. Embree, and L. N. Trefethen:
Piecewise continuous Toeplitz matrices and operators: slow approach to infinity.
SIAM J. Matrix Analysis Appl. 24, 484-489 (2002).

114.
A. Böttcher:
Essay on Bernd Silbermann.
Operator Theory: Adv. and Appl. 135, 1-12 (2002).

113.
A. Böttcher:
On the determinant formulas by Borodin, Okounkov, Baik, Deift, and Rains.
Operator Theory: Adv. and Appl. 135,  91-99 (2002).

112.
A. Böttcher, S. Grudsky, and A. Kozak:
On the distance of a large Toeplitz band matrix to the nearest singular matrix.
Operator Theory: Adv. and Appl. 135, 101-106 (2002).

111.
A. Böttcher and S. Grudsky:
Can spectral value sets of Toeplitz band matrices jump?
Linear Algebra Appl. 351/352, 99-116 (2002).

110.
A. Böttcher, M. Embree, and M. Lindner:
Spectral approximation of banded Laurent matrices with localized random perturbations.
Integral Equations and Operator Theory 42,
142-165 (2002).

109.
A. Böttcher, M. Embree, and V. I. Sokolov:
Infinite Toeplitz and Laurent matrices with localized impurities.
Linear Algebra Appl. 343/344, 101-118 (2002).

108.
A. Böttcher and Yu. I. Karlovich:
Cauchy's singular integral operator and its beautiful spectrum.
Operator Theory: Adv. and Appl. 129, 109-142 (2001).

107.
A. Böttcher and S. Grudsky:
Condition numbers of large Toeplitz-like matrices.
Contemp. Math. 280,
273-299 (2001).

106.
A. Böttcher, S. Grudsky, and I. Spitkovsky:
Toeplitz operators with frequency modulated semi-almost periodic symbols.
J. Fourier Analysis Appl. 7, 523-535 (2001).

105.
A. Böttcher and M. Seybold:
Discrete one-dimensional zero-order pseudodifferential operators on spaces with Muckenhoupt weight.
Algebra i Analiz 13, 116-129 (2001) and
 St. Petersburg Math. J. 13, 241-252 (2002).

104.
A. Böttcher:
One more proof of the Borodin-Okounkov formula for Toeplitz determinants.
Integral Equations and Operator Theory 41, 123-125 (2001).

103.
A. Böttcher, Yu. I. Karlovich, and I. Spitkovsky:
Toeplitz operators with semi-almost periodic matrix symbols on Hardy spaces.
Acta Applicandae Mathematicae 65, 115-136 (2001).

102.
A. Böttcher, A. V. Chithra, and M. N. N. Namboodiri:
Approximation of approximation numbers by truncation.
Integral Equations and Operator Theory 39, 387-395 (2001).

101.
A. Böttcher, Yu. I. Karlovich, and V. S. Rabinovich:
Singular integral operators with complex conjugation from the viewpoint of  pseudodifferential operators.
Operator Theory: Adv. and Appl. 121, 36-59
 (2001).

100.
A. Böttcher and S. Grudsky:
Twenty old and new asymptotic results on Toeplitz band matrices.
In: Structured Matrices: Recent Developments in Theory and Computation
(D. A. Bini, E. Tyrtyshnikov, P. Yalamov, eds.), pp. 1-10,
Nova Science Publishers, Huntington, NY, 2001.

99.
A. Böttcher:
C*-algebras in numerical analysis.
Irish Math. Soc. Bulletin 45, 57-133
(2000).

98.
A. Böttcher and M. Seybold:
Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight.
Studia Math. 143, 121-144 (2000).

97.
A. Böttcher, S. Grudsky, and I. Spitkovsky:
The spectrum is discontinuous on the manifold of Toeplitz operators.
Archiv d. Math. 75, 46-52 (2000).

96.
A. Böttcher, S. Grudsky, and I. Spitkovsky:
Matrix functions with arbitrarily prescribed left and right partial indices.
Integral Equations and Operator Theory 36, 71-91 (2000).

95.
A. Böttcher, S. Grudsky, and I. Spitkovsky:
On the Fredholm indices of associated systems of Wiener-Hopf equations.
J. Integral Equations Appl. 12, 1-29 (2000).

94.
A. Böttcher, Yu. I. Karlovich, and V. S. Rabinovich:
The method of limit operators for one-dimensional singular integrals with slowly oscillating data.
J. Operator Theory 43, 171-198 (2000).

93.
A. Böttcher and S. Grudsky:
Eighteen old and new asymptotic results on Toeplitz band matrices.
In:
Large-Scale Scientific Computations of Engineering and Environmental
Problems II (M. Griebel, S. Margenov, P. Yalamov, eds.), pp. 65-71,
Vieweg, Braunschweig 2000.

92.
A. Böttcher and M. Seybold:
Wackelsatz and Stechkin's inequality for discrete Muckenhoupt weights.
Preprint 99-7, 12 pages, TU Chemnitz, Fakultät für Mathematik, Chemnitz
1999 (will not be submitted for publication; contains full proofs to two
basic theorems used in paper No. 98).

91.
A. Böttcher, S. Grudsky, A. Kozak, and B. Silbermann:
Convergence speed estimates for the norms of the inverses of large truncated Toeplitz matrices.
Calcolo 36, 103-122 (1999).

90.
A. Böttcher, S. Grudsky, A. Kozak, and B. Silbermann:
Norms of large Toeplitz band matrices.
SIAM J. Matrix Analysis Appl. 21,
547-561 (1999).
 
 


With Sergei Grudsky and Ilya Spitkovsky in my office
 
 

89.
A. Böttcher and S. Grudsky:
Toeplitz band matrices with exponentially growing condition numbers.
Electronic Journal of Linear Algebra (ELA) 5, 104-125 (1999).

88.
C.J. Bishop, A. Böttcher, Yu. I. Karlovich, and I. Spitkovsky:
Local spectra and index  of singular integral operators with piecewise
continuous coefficients on composed curves.
Math. Nachr. 206, 5-83 (1999).

87.
A. Böttcher and  Yu. I. Karlovich:
Toeplitz operators with PC symbols on general Carleson Jordan curves
with arbitrary Muckenhoupt weights.
Trans. Amer. Math. Soc.
351, 3143-3196 (1999).

86.
A. Böttcher:
On the corona theorem for almost periodic functions.
Integral Equations and Operator Theory 33, 253-272 (1999).


***** *****

The total solar eclipse of 11 August 1999. I took these two pictures with
a usual autofocus camera in Ensheim (Saar).  Here is some corona mathematics.


85.

A. Böttcher and S. Grudsky:
On the composition of Muckenhoupt weights and inner functions.
J. London Math. Soc. 58, 172-184 (1998).

84.
A. Böttcher and S. Grudsky:
On the condition numbers of large semi-definite Toeplitz matrices.
Linear Algebra Appl. 279, 285-301 (1998).

83.
A. Böttcher, Yu. I. Karlovich, and V. S. Rabinovich:
Mellin pseudodifferential operators with slowly varying symbols
and singular integrals on Carleson curves with Muckenhoupt weights.

Manuscripta Mathematica 95, 363-376  (1998).

82.
A. Böttcher and  Yu. I. Karlovich:
The algebra of singular integral operators on a Lebesgue space with
a Muckenhoupt weight on a closed Carleson curve (Russian).
Dokl. Akad. Nauk 359, 151-154 (1998);
Engl. transl. in
Doklady Math. 57, 193-196 (1998).

81.
A. Böttcher:
On the approximation numbers of large Toeplitz matrices.
Documenta Mathematica 2, 1-29  (1997).

80.
A. Böttcher, S. Grudsky, and B. Silbermann:
Norms of inverses, spectra, and pseudospectra of large truncated
Wiener-Hopf operators and Toeplitz matrices.
New York J. Math. 3, 1-31  (1997).

79.
A. Böttcher and  Yu. I. Karlovich:
The algebra of singular integral operators on the Lebesgue space
on a closed Carleson curve (Russian).
Dokl. Akad. Nauk 357, 7-10 (1997);

Engl. transl. in  Doklady Math. 56, 813-816  (1997).
 

With Yuri Karlovich in Key West

78.
A. Böttcher and H. Wolf:
Spectral approximation for Segal-Bargmann space Toeplitz operators.
In: Linear Operators, Banach Center Publ., Vol. 38, pp. 25-48, PAN,
Warsaw 1997.

77.
A. Böttcher:
Review of  ''Spectral Theory of Approximation Methods for Convolution
Operators'' by R. Hagen, S. Roch,  and B. Silbermann.

Bull. Amer. Math. Soc.
33, 237-243 (1996).

76.
A. Böttcher:
Infinite matrices and projection methods.
In: Lectures on Operator Theory
and Its Applications (P. Lancaster, ed.), pp. 1-72,
Fields Institute Monographs,
Vol. 3, Amer. Math. Soc., Providence, RI, 1996.

75.
A. Böttcher and H. Heidler:
Characteristic polynomials of composition operators.
In: Proc. European
Conf. on Iteration Theory, Batschuns, Austria, 1992, pp. 279-280,
World
Scientific Publishing Co., Singapore 1996.

74.
A. Böttcher and  Yu. I. Karlovich:
Toeplitz and singular integral operators on general Carleson Jordan curves.
Operator Theory: Adv. and Appl. 90, 119-152  (1996).

73.
A. Böttcher and S. Grudsky:
Toeplitz operators with discontinuous symbols: phenomena beyond piecewise discontinuity.
Operator Theory: Adv. and Appl. 90, 55-118 (1996).

72.
A. Böttcher,  I. Gohberg, Yu. I. Karlovich, N. Krupnik, S. Roch,
B. Silbermann, and I. Spitkovsky:
Banach algebras generated by N idempotents and applications.
Operator Theory: Adv. and Appl. 90, 19-54  (1996).

71.
A. Böttcher, Yu. I. Karlovich, and V. S. Rabinovich:
Emergence, persistence, and disappearance of logarithmic spirals in the
spectra of singular integral operators.
Integral Equations and Operator
Theory 25, 406-444 (1996).

70.
A. Böttcher:
Mathematischer Beweis versus Computerexperiment.
In: Wiss. Kolloquium "Zum Nutzen von Grundlagenforschung",
Villa Hügel, 30. November 1995, pp. 39-42, Krupp-Stiftung, Essen 1996.

69.
A. Böttcher and Yu. I. Karlovich:
Submultiplicative functions and spectral theory of Toeplitz operators.
Integral Transforms and Special Functions 4, 181-202 (1996).

68.
A. Böttcher and H. Wolf:
Polynomial collocation over massive sets for Toeplitz integral equations on the Bergman space.
J. Computational and Applied Math. 66, 89-96 (1996).

67.
A. Böttcher and B. Silbermann:
Infinite Toeplitz and Hankel matrices with operator-valued symbols.
SIAM J. Math. Analysis 27, 805-822 (1996).

66.
A. Böttcher:
Toeplitz operators with piecewise continuous symbols - a neverending story?
Jahresbericht der DMV 97, 115-129 (1995).
 

With Yuri Karlovich in Barcelona

65.
A. Böttcher and Yu. I. Karlovich:
Toeplitz and singular integral operators on Carleson curves with logarithmic whirl points.
Integral Equations and Operator Theory 22, 127-161 (1995) .

64.
A. Böttcher and H. Heidler:
Algebraic and essentially algebraic composition operators on C(X).
Aequationes Mathematicae 49, 276-294 (1995).

63.
A. Böttcher and H. Wolf:
Analytic element collocation over geodesic circles for Bergman space Toeplitz operators.
In: Proc. Internat. Conf. Differential
Geometry, Hamiltonian Systems,
and Operator Theory, Kingston, Jamaica,
 1994, pp. 69-87,
University of the West Indies Press, Mona 1995.

62.
A. Böttcher:
The Onsager formula, the Fisher-Hartwig conjecture, and their
influence on research into Toeplitz operators.

J. Statist. Physics
78 (Lars Onsager Festschrift), 575-585 (1995).

61.
A. Böttcher:
Pseudospectra and singular values of large convolution operators.
J. Integral Equations Appl. 6, 267-301 (1994).

60.
A. Böttcher and I. Spitkovsky:
Pseudodifferential operators with heavy spectrum.
Integral
Equations and Operator Theory 19, 251-269 (1994).

59.
A. Böttcher, B. Silbermann, and H. Widom:
Determinants of truncated Wiener-Hopf operators with
Hilbert-Schmidt kernels and piecewise continuous symbols.

Archiv d. Math. 63, 60-71 (1994).

58.
A. Böttcher, B. Silbermann, and H. Widom:
A continuous analogue of the Fisher-Hartwig formula for piecewise continuous symbols.
J. Funct. Analysis 122, 222-246 (1994).

57.
A. Böttcher and B. Silbermann:
Operator-valued Szegö-Widom limit theorems.
Operator Theory:
Adv. and Appl. 71, 33-53 (1994).

56.
A. Böttcher and H. Widom:
Two remarks on spectral approximations for Wiener-Hopf operators.
J. Integral Equations Appl. 6, 31-36 (1994).

My Erdös number is 3.

55.
A. Böttcher, Yu. I. Karlovich, and I. Spitkovsky:
Toeplitz operators with semi-almost periodic symbols on spaces with Muckenhoupt weight.
Integral Equations and Operator Theory
18, 261-276 (1994).
 

Dinner with Ilya Spitkovsky and Yuri Karlovich
 

54.
A. Böttcher, Yu. I. Karlovich,  and B. Silbermann:
Singular integral operators with PQC coefficients and freely transformed argument.
Math. Nachr. 166, 113-133 (1994).

53.
A. Böttcher:
Magnete, Determinanten und Fourier-Summen.
Spektrum der
Wissenschaft 3/1994, 25-27 (1994).

52.
A. Böttcher and H. Wolf:
Asymptotic invertibility of Bergman and Bargmann space Toeplitz operators.
Asymptotic Analysis 8, 15-33 (1994).

51.
A. Böttcher and B. Silbermann:
Axler-Chang-Sarason-Volberg theorems for harmonic approximation and stable convergence.
In: Linear and Complex Analysis Problem Book 3,

Part I (V. P. Havin, N. K. Nikolski, eds.), pp. 340-341,
Lecture Notes
in Math., Vol. 1573, Springer-Verlag 1994.

50.
A. Böttcher and H. Heidler:
Classification of finite-dimensional algebras generated by the
Calkin image of a composition operator on l^p with weight.

Algebra i Analiz 5, 69-96 (1993) and St. Petersburg Math. J. 5, 1099-1119 (1994).

49.
A. Böttcher:
Toeplitz operators on the disk with locally sectorial symbols.
Rocky Mountain J. Math. 23, 803-816 (1993).

48.
A. Böttcher and I. Spitkovsky:
On a theorem of Rooney concerning the spectrum of the singular integral operator.
Z. Analysis Anw. 12, 93-96 (1993).

47.
A. Böttcher and H. Wolf:
Galerkin-Petrov methods for Bergman space Toeplitz operators.
SIAM J. Numer. Analysis 30, 846-863 (1993).

46.
A. Böttcher and I. Spitkovsky:
Wiener-Hopf integral operators with PC symbols on spaces with Muckenhoupt weight.
Revista Matematica Iberoamericana 9, 257-279 (1993).

45.
A. Böttcher and H. Wolf:
Interpolation in the Bergman space, mean values of harmonic functions,
and an inverse problem of potential theory.
Wiss. Z. TU Chemnitz
34, 31-35 (1992).

44.
A. Böttcher and H. Heidler:
Algebraic composition operators.
Integral Equations and Operator
Theory 15, 389-411 (1992).

43.
A. Böttcher and H. Wolf:
Collocation methods for Toeplitz operators on Dzhrbashyan spaces (Russian).
Bull. Armen. Acad. Sci. 93, 168-172 (1992).

42.
A. Böttcher and H. Wolf:
Large sections of Bergman space Toeplitz operators with piecewise continuous symbols.
Math. Nachr. 156, 129-155 (1992).

41.
A. Böttcher:
Invertible values of elementary operators and projection methods for Toeplitz operators.
In:  Proc. Internat. Conf. on Elementary Operators,
 Blaubeuren 1991,  pp. 157-161,
World Scientific Publishing Co.,
Singapore 1992.

40.
A. Böttcher and H. Wolf:
Finite sections of segal-Bargmann space Toeplitz operators with polyradially continuous symbols.
Bull. Amer. Math. Soc. 25, 365-372 (1991).

39.
A. Böttcher and I. Spitkovsky:
Toeplitz operators with  PQC symbols on weighted Hardy spaces.
J. Funct. Analysis 97, 194-214 (1991).

38.
A. Böttcher, S. Roch, B. Silbermann, and I. Spitkovsky:
A Gohberg-Krupnik-Sarason symbol calculus for algebras of Toeplitz,
Hankel, Cauchy, and Carleman operators.
Operator Theory: Adv. and
Appl. 48, 189-234 (1990).

37.
A. Böttcher, B. Silbermann, and I. Spitkovsky:
Toeplitz operators with piecewise quasisectorial symbols.
Bull. London Math.
Soc. 22, 281-286 (1990).

36.
A. Böttcher:
Truncated Toeplitz operators on the polydisk.
Monatshefte f. Math. 110,
23-32 (1990).

35.
A. Böttcher and H. Heidler:
On linear functional equations with two involutions.
Seminar Analysis 1989/90,
31-43 (1990).

34.
A. Böttcher:
Status report on rationally generated block Toeplitz and Wiener-Hopf determinants.
Unpublished manuscript, 1989.

33.
A. Böttcher:
Wiener-Hopf determinants with rational symbols. 
Math. Nachr. 144,
39-64 (1989).

32.
A. Böttcher:
On Mikaelyan's conjecture in the theory of Wiener-Hopf-determinants (Russian).
Izv. Armen. Akad. Nauk 24, 188-192 (1989); Engl. transl. in

Sov. J. Contemp. Math. Anal., Arm. Acad. Sci. 24, 85-89 (1989).

31.
A. Böttcher and S. Dzhirgalova:
On Wiener-Hopf determinants with rational matrix symbols.
Seminar Analysis 1988/89, 21-39 (1989).

30.
A. Böttcher, N. Krupnik, and B. Silbermann:
A general look at local principles with special emphasis on the norm computation aspect.
Integral Equations and Operator Theory 11, 455-479 (1988).

29.
A. Böttcher and B. Silbermann:
Asymptotics of Toeplitz and Wiener-Hopf operators.
In: Proc. 9th Conf.
 Probl. and Meth. in Math. Phys., Karl-Marx-Stadt 1988, pp. 27-35,
Teubner
1988.

28.
A. Böttcher:
Asymptotic formulas for rationally generated block Toeplitz determinants.
Seminar Analysis 1987/88, 1-13 (1988).

27.
A. Böttcher and B. Silbermann:
Toeplitz operators with symbols from C+H^\infty in the spaces l^p (Russian).
Zap. Nauchn. Sem. LOMI 157, 124-128 (1987);

Engl. transl. in  J. Soviet Math. 44, 834-836 (1989).

26.
A. Böttcher:
Multidimensional Toeplitz operators with locally sectorial symbols.
Seminar Analysis 1986/87, 1-16 (1987).

25.
A. Böttcher and B. Silbermann:
Local spectra of approximate identities, cluster sets, and Toeplitz operators.
Wiss. Zeitschr. TH Karl-Marx-Stadt 28, 175-180 (1986).

24.
A. Böttcher:
On Toeplitz operators generated by symbols with three essential cluster points.
Preprint P-Math-04/86, 22 pages, Karl-Weierstrass-Institut,

Berlin 1986 (never published but often cited).

23.
A. Böttcher and B. Silbermann:
Toeplitz operators and determinants generated by symbols with one Fisher-Hartwig singularity. 
Math. Nachr. 127, 95-124 (1986).

22.
A. Böttcher, S. Roch, and B. Silbermann:
Local constructions and Banach algebras associated with Toeplitz operators on H^p. 
Seminar Analysis 1985/86, 23-30 (1986).

21.
A. Böttcher:
A remark on the relation between the partial indices of a matrix
function and its harmonic extension.
Seminar Analysis 1985/86,
19-22 (1986).

20.
A. Böttcher:
Scalar Toeplitz operators, distance estimates, and localization over subalgebras of C+H^\infty.
Seminar Analysis 1985/1986, 1-17 (1986).

19.
A. Böttcher and B. Silbermann:
Toeplitz matrices and determinants with Fisher-Hartwig symbols.
J. Funct. Analysis 63, 178-214 (1985).

18.
A. Böttcher and B. Silbermann:
Toeplitz determinants generated by symbols with one singularity of  Fisher-Hartwig type. 
Wiss. Zeitschr. TH Karl-Marx-Stadt 26, 186-188
(1984).

17.
A. Böttcher and B. Silbermann:
Toeplitz determinants with symbols from the Fisher-Hartwig class (Russian).
Dokl. Akad. Nauk SSSR 278, 13-16 (1984);
Engl.
transl. in Soviet Math. Dokl. 30, 301-304 (1984).

16.
A. Böttcher:
The finite section method for two-dimensional Wiener-Hopf operators
in L^p with piecewise continuous symbols.

Math. Nachr. 116, 61-73
(1984).

15.
A. Böttcher:
The finite section method for Wiener-Hopf integral operators with
piecewise continuous symbols in the spaces L^p (Russian).
Funkts. Anal. Prilozh. 18, 55-56 (1984);
Engl. transl. in
Funct. Anal. Appl. 18, 132-133 (1984).

14.
A. Böttcher:
Fredholmness and finite section method for Toeplitz operators in  l^p(Z_+ \times Z_+), II.
Z. Analysis Anw. 3, 191-202 (1984).

13.
A. Böttcher:
Fredholmness and finite section method for Toeplitz operators in l^p(Z_+ \times Z_+).
Z. Analysis Anw. 3, 97-110 (1984).

12.
A. Böttcher:
Das Reduktionsverfahren für nichtelliptische Wiener-Hopf'sche
Integraloperatoren in einer Klasse von topologischen Vektorräumen.
Wiss. Zeitschr. TH Karl-Marx-Stadt 25, 308-312 (1983).

11.
A. Böttcher:
Fredholm theory and finite section method for two-dimensional
Wiener-Hopf operators with piecewise continuous symbols (Russian).
Dokl. Akad. Nauk SSSR 273, 1298-1300 (1983);
Engl. transl. in
Soviet Math. Dokl. 28, 773-776 (1983).

10.
A. Böttcher:
Two-dimensional convolutions in angles with kernels supported in a half-plane (Russian).
Matem. Zametki 34, 207-218 (1983);
Engl. transl. in  Math. Notes
34, 585-591 (1983).

9.
A. Böttcher and B. Silbermann:
The finite section method for Toeplitz operators on the quarter-plane with piecewise continuous symbols.
Math. Nachr. 110, 279-291 (1983).

8.
A. Böttcher and B. Silbermann:
Wiener-Hopf determinants with symbols having zeros of analytic type.
Seminar Analysis 1982/83, 224-243 (1983) .

7.
A. Böttcher:
Toeplitzdeterminanten in der statistischen Physik.
In:  Ergebnisse d. Schule
 Junger Wissenschaftler zur Math. Physik, pp. 19-21,
Pruchten 1982.

6.
A. Böttcher:
On two-dimensional Wiener-Hopf integral equations with a degenerate symbol (Russian).
Math. Nachr. 109, 195-213 (1982).

5.
A. Böttcher and A. E. Pasenchuk:
On the invertibility of Wiener-Hopf operators on the quarter-plane (Russian).
In:  Differential and Integral Equations, pp. 9-19, Elista 1982.

4.
A. Böttcher:
Toeplitz determinants with piecewise continuous generating function.
Z. Analysis Anw. 1, 23-39 (1982).

3.
A. Böttcher and B. Silbermann:
Über das Reduktionsverfahren für diskrete Wiener-Hopf-Gleichungen mit unstetigem Symbol.
Z. Analysis Anw. 1, 1-5 (1982).

2.
A. Böttcher and B. Silbermann:
The asymptotic behavior of Toeplitz determinants for generating functions with zeros of integral orders.
Math. Nachr. 102, 79-105 (1981).

1.
A. Böttcher and B. Silbermann:
Notes on the asymptotic behavior of block Toeplitz matrices and determinants.
Math. Nachr. 98, 183-210 (1980).

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