Toeplitz Centennial: Toeplitz Memorial Conference in Operator Theory, Dedicated to the 100th Anniversary of the Birth of Otto Toeplitz, Tel Aviv, May 11–15, 1981

568 Pages·1982·12.45 MB·German

by  I. Gohberg (auth.)

OT4:
Operator Theory: Advances and Applications
Vol.4
Edited by
I.Gohberg
Editorial Board
K.Clancey B.Gramsch M. Livsic
L.Cobum W.Helton E. Meister
R.Douglas D. Herrero B. Mityagin
H.Dym M.Kaashoek J. Pincus
A.Dynin T. Kailath M. Rosenblum
P. Fillmore H.Kaper J.Rovnjak
C. Foias S.Kuroda D. Sarason
P.Fuhrmann P. Lancaster H.Widom
S. Goldberg L. Lerer D.Xia
Honorary and Advisory
Editorial Board
P.Halmos R. Phillips
T.Kato B. Sz.-Nagy
S.Mikhlin
Editorial Office
School of Mathematical Sciences
Tel-Aviv University
Ramat-Aviv (Israel)
Springer Basel AG
Toeplitz Centennial
Toeplitz Memorial Conference in Operator Theory,
Dedicated to the tOOth Anniversary of the Birth of
Otto Toeplitz, Tel Aviv, May 11-15, 1981
Edited by
I. Gohberg
Springer Basel AG
1982
Volume Editorial Office
School of Mathematical Sciences
Tel-Aviv University
Ramat-Aviv (Israel)
Library of Congress Cataloging in Publication Data
Toeplitz Memorial Conference in Operator
Theory (1981 : Tel Aviv (Israel)
Toeplitz centennial.
(Operator theory, advances and applications ;
4)
1. Operator theory--Congresses.
2. Toeplitz, Otto, 1881-1940. I. Gokhberg,
I. TS. (Izrail TSudikovich), 1928-
II. Title. III. Series.
QA329.T63 1981 515.7'24 82-1319
ISBN 978-3-0348-5184-8 AACR2
CIP-Kurztitelaufnahme der Deutschen Bibliothek
Toeplitz centennial/Toeplitz Memorial Conference
in Operator Theory, dedicated to the lOOth
anniversary of the birth of Otto Toeplitz,
Tel Aviv, May 11-15, 1981, Vol. ed. I. Gohberg.
[Vol. editorial office School of
Mathemat. Sciences, Tel-Aviv Univ. (Israel)).
Basel; Boston; Stuttgart: Birkhauser, 1982.
(Operator theory; Vol. 4)
ISBN 978-3-0348-5184-8
NE: Gochberg, Iszrail' C. [Hrsg.); Toeplitz
Memorial Conference in Operator Theory< 1981,
Tel-Aviv>; GT
All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system,
or transmitted in any form or by any means, electronic, mechanical, photocopying,
recording or otherwise, without the prior permission of the copyright owner.
© Springer Basel AG 1982
Originally published by Birkhauser Varlag Basel in 1982
Softcover reprint of the hardcover 1st edition 1982
ISBN 978-3-0348-5184-8 ISBN 978-3-0348-5183-1 (eBook)
DOI 10.1007/978-3-0348-5183-1
Otto Toeplitz 1881-1940
7
PREFACE
The conference is now over and enough time has passed for
us to realize that the concensus of opinion of the participants
is that it was indeed a successful and fruitful conference.
This conference showed just how wide spread are the ideas of
Otto Toeplitz, and how strong an influence his work has.
The majority of participants contributed papers for this
volume, which will help to bring to this interesting conference
a wider audience. About the background and organization of
the conference, the reader can learn from the opening address,
which is included in place of an introduction.
In my opinion this volume would be of interest to a wide
public; experts in pure and applied mathematics as well as
persons interested in the history of mathematics. The papers
are divided into two sections. The first section is given to
research papers, and the second to memorial papers.
We are indebted to Professor G. K8the who allowed us to
publish in the section of memorial papers the translation into
English of his talk, given at a Colloquium in honour of Otto
Toeplitz in Bonn. During the preparation of this volume great
assistance was extended to us by Dr. Uri Toeplitz and Mrs. G.
Riesel to whom I would like to express my sincere gratitude.
I would like to take this opportunity to thank all persons
and organizations who helped to make this conference such a
success, and also Birkhauser Verlag for publishing this volume
of the Proceedings.
I. Gohberg
9
CONTENTS
GOHBERG, I. Opening Address . . . . . . . • . • . . . . . . 13
RESEARCH PAPERS
ALBRECHT, E. Decomposable System of Operators
in Harmonic Analysis 19
AROCENA, R. Generalized Toeplitz Kernels and
COTLAR, M. Adamjan-Arov-Krein Moment Problems . • . . . . . 37
AZOFF, E. Singular Points of Families of
CLANCEY, K. Fredholm Integral Operators 57
GOHBERG, I.
BALL, J.A. A Noneuclidean Lax-Beurling Theor~m
with Applications to Matricial
Nevanlinna-Pick Interpolation . 67
BART, H. Wiener-Hopf Integral Equations,
GOHBERG, I. Toeplitz Matrices and Linear
KAASHOEK, M.A. Systems •.........•. 85
BAUM, P. Toeplitz Operators and Poincare
DOUGLAS, R.G. Duality . . . . . • . . • . . . . . . . . . 137
BROWN, L.G. Classification of Operators on
Finite Dimensional Hilbert Spaces,
Generalized Finite Toeplitz
Matrices, and Szego Polynomials ...... 167
CLARK, D.N. Quasisimilarity of Rational
Toeplitz Operators 175
COBURN, L.A. The Koecher Norm and Toeplitz
Operators in Several Variables 187
CORDES, H;O. Global Parametrices for Certain
Singular Elliptic Operators . . . . . . • . . . 193
10
COSTABEL, M. On the Algebra Generated by Singular
Integral Operators with Piecewise
Continuous Coefficients •.•.....••.. 211
DAVIS, C. A Factorization of an Arbitrary
m x n Contractive Operator-Matrix ••...•. 217
DYM, H. Applications of Factorization and
IACOB, A. Toeplitz Operators to Inverse
Problems . • • • • • •.. 233
FOIAS, C. Toeplitz Operators and the Theory of
Homogenization for Partial Differential
Equations ..•..•..•...•.• 261
GAUCHMAN H. Operator colligations on Differentiable
I
Manifolds 271
HALLER, H. Extension of Otto Toeplitz' Combinatorial
JACOBS, K. Construction of Almost
Periodic Functions on the Real Line 303
KABALLO, W. On Fredholm Operator Valued ~-
Functions • 313
KAILATH, T. Generalized Schur Parametrization
LEV-ARI, H. of Nonstationary Second-Order
Processes • 321
KALMAN, R.E. Realization of Covariance Sequences 331
KAPER, H.G. Factorization Methods in Linear
Transport Theory . . . • 343
LAX, P.O. The Asymptotic Distribution of
PHILLIPS, R.f Lattice Points in Euclidean and Non
Euclidean Spaces • . . . • . . 365
LIV~IC, M.S. Commuting Operators and Fields of
Systems, Distributed in Euclidean
Space 377
LUMER, G. Local Dissipativeness and Closure
of Local Operators • . • • . . . • 415
MEISTER, E. Multiple-Part Wiener-Hopf Operators
with Some Applications in Mathematical
Physics .••. • . . • 427
PUTNAM, C.R. The Spectrum of the Absolute Value of
a Hyponormal Operator . . • • . • . . • . • • . 449
11
WAELBROECK, L. Galbs, Tensor Products, and Convex
Holomorphic Mappings . • • . . • 463
WIDOM, H. On a Class of Integral Operators
with Discontinuous Symbol • • . . 477
WOLFF, M. Group Actions on Banach Lattices and
Applications to Dynamical Systems 501
ZWEIFEL, P.F Resolvent Integration Methods in
GREENBERG, W. Transport Theory . . • . . . . . 525
MEMORIAL PAPERS
KOTHE, G. In Memory of Otto Toeplitz 545
TOEPLITZ, U. Some Reminiscences • • . 557
DIEUDONNE, J. Otto Toeplitz' Formative Years 565
KOTHE, G. Toeplitz and the Theory of
Sequence Spaces 575
PROGRAMME OF THE CONFERENCE . . • • . . • • 585