Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics: The Albrecht Böttcher Anniversary Volume

757 Pages·2017·16.43 MB·English

by  Dario A. Bini

Operator Theory
Advances and Applications
259
Dario A. Bini
Torsten Ehrhardt
Alexei Yu. Karlovich
Ilya Spitkovsky
Editors
Large Truncated
Toeplitz Matrices,
Toeplitz Operators,
and Related Topics
The Albrecht Böttcher Anniversary
Volume

Operator Theory: Advances and Applications
Volume 259

Founded in 1979 by Israel Gohberg

Editors:
Joseph A. Ball (Blacksburg, VA, USA)
Harry Dym (Rehovot, Israel)
Marinus A. Kaashoek (Amsterdam, The Netherlands)
Heinz Langer (Wien, Austria)
Christiane Tretter (Bern, Switzerland)

Associate Editors: Honorary and Advisory Editorial Board:
Vadim Adamyan (Odessa, Ukraine) Lewis A. Coburn (Buffalo, NY, USA)
Wolfgang Arendt (Ulm, Germany) Ciprian Foias (College Station, TX, USA)
Albrecht Böttcher (Chemnitz, Germany) J.William Helton (San Diego, CA, USA)
B. Malcolm Brown (Cardiff, UK) Thomas Kailath (Stanford, CA, USA)
Raul Curto (Iowa, IA, USA) Peter Lancaster (Calgary, Canada)
Fritz Gesztesy (Columbia, MO, USA) Peter D. Lax (New York, NY, USA)
Pavel Kurasov (Stockholm, Sweden) Donald Sarason (Berkeley, CA, USA)
Vern Paulsen (Houston, TX, USA) Bernd Silbermann (Chemnitz, Germany)
Mihai Putinar (Santa Barbara, CA, USA) Harold Widom (Santa Cruz, CA, USA)
Ilya Spitkovsky (Abu Dhabi, UAE)

Subseries
Linear Operators and Linear Systems
Subseries editors:
Daniel Alpay (Orange, CA, USA)
Birgit Jacob (Wuppertal, Germany)
André C.M. Ran (Amsterdam, The Netherlands)

Subseries
Advances in Partial Differential Equations
Subseries editors:
Bert-Wolfgang Schulze (Potsdam, Germany)
Michael Demuth (Clausthal, Germany)
Jerome A. Goldstein (Memphis, TN, USA)
Nobuyuki Tose (Yokohama, Japan)
Ingo Witt (Göttingen, Germany)
Moreinformationaboutthisseriesathttp://www.springer.com/series/4850
Dario A. Bini • Torsten Ehrhardt
Alexei Yu. Karlovich • Ilya Spitko v sky
Editors
Large Truncated Toeplitz
Matrices, Toeplitz
Operators, and Related Topics
The Albrecht Böttcher Anniversary Volume
Editors
Dario A. Bini Torsten Ehrhardt
Dipartimento di Matematica Mathematics Department
Università di Pisa University of California
Pisa, Italy Santa Cruz, California, USA
Alexei Yu. Karlovich Ilya Spitkovsky
Departamento de Matemática New York University Abu Dhabi
Faculdade de Ciências e Tecnologia Abu Dhabi, United Arab Emirates
Universidade Nova de Lisboa
Caparica, Portugal
ISSN 0255-0156 ISSN 2296-4878 (electronic)
Operator Theory: Advances and Applications
ISBN 978-3-319-49180-6 ISBN 978-3-319-49182-0 (eBook)
DOI 10.1007/978-3-319-49182-0

Library of Congress Control Number: 2017934911
Mathematics Subject Classification (2010): 15B05, 47B35, 60B20

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Contents
Preface .................................................................. ix
Publications of Albrecht Bo¨ttcher ........................................ xi
S. Grudsky
Albrecht Bo¨ttcher – 20 Years of Friendship and Joint Work ......... 1
J. Jahns
Salutatory with Regards from the Mathematics
Students of Chemnitz ............................................... 19
B. Silbermann
Essay on Albrecht Bo¨ttcher ......................................... 21
F.-O. Speck
Meeting Albrecht the Strong ........................................ 37
I. Spitkovsky
The Beginning (the Way I Remember it) ............................ 41
D. Wenzel
Personal Address on the Occasion of Albrecht Bo¨ttcher’s
60th Birthday ...................................................... 47
M. Barrera and S.M. Grudsky
Asymptotics of Eigenvalues for Pentadiagonal Symmetric
Toeplitz Matrices ................................................... 51
H. Bart, T. Ehrhardt and B. Silbermann
Echelon Type Canonical Forms in Upper Triangular
Matrix Algebras .................................................... 79
E. Basor and T. Ehrhardt
Asymptotic Formulas for Determinants of a Special Class of
Toeplitz + Hankel Matrices ......................................... 125
vi Contents
D.A. Bini and B. Meini
Generalization of the Brauer Theorem to Matrix Polynomials
and Matrix Laurent Series .......................................... 155
J.M. Bogoya, S.M. Grudsky and E.A. Maximenko
Eigenvalues of Hermitian Toeplitz Matrices Generated by
Simple-loop Symbols with Relaxed Smoothness ..................... 179
T. Bothner, P. Deift, A. Its and I. Krasovsky
On the Asymptotic Behavior of a Log Gas in the Bulk Scaling
Limit in the Presence of a Varying External Potential II ............. 213
D. Bump, P. Diaconis, A. Hicks, L. Miclo and H. Widom
Useful Bounds on the Extreme Eigenvalues and Vectors of
Matrices for Harper’s Operators ..................................... 235
T. Ehrhardt and K. Rost
Fast Inversion of Centrosymmetric Toeplitz-plus-Hankel
Bezoutians .......................................................... 267
B. Fritzsche, B. Kirstein and C. M¨adler
On Matrix-valued Stieltjes Functions with an Emphasis on
Particular Subclasses ............................................... 301
C. Garoni and S. Serra-Capizzano
The Theory of Generalized Locally Toeplitz Sequences:
a Review, an Extension, and a Few Representative Applications ..... 353
G.J. Groenewald, S. ter Horst and M.A. Kaashoek
The B´ezout Equation on the Right Half-plane in a Wiener
Space Setting ....................................................... 395
P. Junghanns and R. Kaiser
On a Collocation-quadratureMethod for the Singular Integral
Equation of the Notched Half-plane Problem ........................ 413
Yu.I. Karlovich
The Haseman Boundary Value Problem with Slowly Oscillating
Coefficients and Shifts .............................................. 463
N. Krupnik and A. Markus
On the Norm of Linear Combinations of Projections and Some
Characterizations of Hilbert Spaces ................................. 501
V. Kryakvin and V. Rabinovich
Pseudodifferential Operators in Weighted Ho¨lder–Zygmund
Spaces of Variable Smoothness ...................................... 511
Contents vii
Z. Lu and D. Wenzel
Commutator Estimates Comprising the Frobenius Norm –
Looking Back and Forth ............................................ 533
E. Militzer, L.J. Patton, I.M. Spitkovsky and M.-C. Tsai
Numerical Ranges of 4-by-4 Nilpotent Matrices: Flat Portions
on the Boundary .................................................... 561
A. Pietsch
Traces on Operator Ideals and Related Linear Forms on Sequence
Ideals (Part IV) ..................................................... 593
D. Potts and M. Tasche
Error Estimates for the ESPRIT Algorithm ......................... 621
S. Roch
The Universal Algebra Generated by a Power Partial Isometry ...... 649
M. Seidel
Norms, Condition Numbers and Pseudospectra of Convolution
Type Operators on Intervals ........................................ 663
F.-O. Speck
Paired Operators in Asymmetric Space Setting ...................... 681
C.A. Tracy and H. Widom
Natural Boundary for a Sum Involving Toeplitz Determinants ....... 703
E. Wegert
A Riemann–Hilbert Approach to Filter Design ...................... 719
Preface
This volume is dedicated to Albrecht Bo¨ttcher on the occasion of his sixtieth
birthday. The first partcontains two essayswritten by SergeiGrudsky andBernd
Silbermann,andseveralpersonalrecollectionswrittenbycolleagues,students,and
friends of Albrecht. The second part consists of twenty four selected scientific pa-
persdevotedtovariousfieldsofAnalysisandMatrixTheory,includingasymptotics
of Toeplitz and Hankel matrices, boundary value problems and singular integral
operators, numerical ranges and pseudospectra, convolution and pseudodifferen-
tialoperators.AlbrechtB¨ottcherhasbeenenrichingalltheseareasbyfundamental
contributions during more than three decades. The volume ends with the contri-
bution by Elias Wegert, who was a classmate of Albrecht in “Spezialklasse fu¨r
Mathematik und Physik, Hochschule Karl-Marx-Stadt”.It tells us about the first
steps of Albrechtin Mathematics. We thank all contributors for their enthusiasm
when preparing the articles for this volume. We feel happy to honour Albrecht
Bo¨ttcherbytheeditionofthisvolume,andwishhimgoodhealth and ever greater
success in his work.
September 2016 Dario A. Bini,
Torsten Ehrhardt,
Alexei Yu. Karlovich,
Ilya Spitkovsky
Albrecht Bo¨ttcher