Systems, Approximation, Singular Integral Operators, and Related Topics: International Workshop on Operator Theory and Applications, IWOTA 2000

535 Pages·2001·14.4 MB·English

by  Daniel Alpay

Operator Theory: Advances and
Applications
Voi. 129
Editor:
1. Gohberg
Editorial Office:
School of Mathematical H.G. Kaper (Argonne)
Sciences S.T. Kuroda (Tokyo)
Tel Aviv University P. Lancaster (Calgary)
Ramat Aviv, Israel L.E. Lerer (Haifa)
B. Mityagin (Columbus)
Editorial Board: V. V. Peller (Manhattan, Kansas)
J. Arazy (Haifa) J. D. Pincus (Stony Brook)
A. Atzmon (Tel Aviv) M. Rosenblum (Charlottesville)
J. A. BaII (Blacksburg) J. Rovnyak (Charlottesville)
A. Ben-Artzi (Tel Aviv) D. E. Sarason (Berkeley)
H. Bercovici (Bloomington) H. Upmeier (Marburg)
A. Bottcher (Chemnitz) S. M. Verduyn Lunei (Leiden)
K. Clancey (Athens, USA) D. Voiculescu (Berkeley)
L. A. Coburn (Buffalo) H. Widom (Santa Cruz)
K. R. Davidson (Waterloo, Ontario) D. Xia (Nashville)
R. G. Douglas (Stony Brook) D. Yafaev (Ren nes)
H. Dym (Rehovot)
A. Dynin (Columbus) Honorary and Advisory
P. A. Fillmore (Halifax) Editorial Board:
P. A. Fuhrmann (Beer Sheva) C. Foias (Bloomington)
S. Goldberg (College Park) P. R. Halmos (Santa Clara)
B. Gramsch (Mainz) T. Kailath (Stanford)
G. Heinig (Chemnitz) P. D. Lax (New York)
J. A. Helton (La Jolla) M. S. Livsic (Beer Sheva)
M.A. Kaashoek (Amsterdam)
Systems, Approximation,
Singular Integral Operators,
and Related Topics
International Workshop on Operator Theory and Applications,
IWOTA2000
Alexander A. Borichev
Nikolai K. Nikolski
Editors
Springer Basel AG
Editors:
Alexander A. Borichev
Nikolai K. Nikolski
Departement de Mathematiques
Universit6 de Bordeaux I
351, cours de la Liberation
33405 Talence
France
2000 Maihematics Subject Classification 30, 34, 35, 41, 42, 43, 46, 47, 93
A CIP catalogue record for this book is available from the
Library of Congress, Washington D.C., USA
Systems, approximation, singular integral operators, and related topics I
International Workshop on Operator Theory and Applications, IWOTA 2000.
Alexander A. Borichev ; Nikolai K. Nikolski, ed .. -Basel ; Boston; Berlin:
Birkhiiuser, 2001
(Operator theory ; VoI. 129)
ISBN 978-3-0348-9534-7 ISBN 978-3-0348-8362-7 (eBook)
DOI 10.1007/978-3-0348-8362-7
This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned,
specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms
or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained.
© 2001 Springer Basel AG
Origina.lly published by Birkhiiuser Verlag in 2001
Softcover reprint ofthe hardcover Ist edition 2001
Printed on acid-free paper produced from chlorine-free pulp. TCF
00
Cover design: Heinz Hiltbrunner, Basel
ISBN 978-3-0348-9534-7
987654321 http://www.birkhauser-science.ch
PREFACE
This book is de
voted to some topical prob
lems and various applica
tions of Operator Theory and
to its interplay with many
other fields of analysis as
modern approximation the
ory, theory of dynamic sys
tems, harmonic analysis and
complex analysis. It consists
of 20 carefully selected sur
veys and research-expository
papers. Their scope gives a
representative status report
on the field drawing a pic
ture of a rapidly developing
domain of analysis. An abun
dance of references completes
the picture.
All papers included
in the volume originate from
lectures delivered at the l1th
edition of the International
Workshop on Operator The
ory and its Applications
(IWOTA-2000, June 13-16,
Bordeaux). Some information
about the conference, including the complete list of participants, can be found on
forthcoming pages.
The editors are indebted to A.Sudakov for helping them in polishing and
assembling original TeX files.
A. Borichev and N. Nikolski
Talence, May 2001
v
vii
International Workshop on Operator Theory and Its Applications
(June 13-June 16, 2000, Universite Bordeaux 1)
The International Workshop on Operator Theory and its Applications
(IWOTA) is a satellite meeting of the international symposium on the Mathe
matical Theory of Networks and Systems (MNTS). In 2000, the MNTS is held in
Perpignan, France, June 19-23. IWOTA 2000 was the eleventh workshop of this
kind.
The previous IWOTA meetings were held in Santa Monica, California, USA
(1981), Rehovot, Israel (1983), Amsterdam, The Netherlands (1985), Mesa, Ari
zona, USA (1987), Rotterdam, The Netherlands (1989), Sapporo, Japan (1991),
Regensburg, Germany (1995), Bloomington, Indiana, USA (1996), Groningen, The
Netherlands (1998).
The international Steering Committee of IWOTA consists of I. Gohberg
(President, Tel Aviv), T. Ando (Sapporo), H. Bart (Rotterdam), H. Bercovici
(Bloomington), R. Dijksma (Groningen), H. Dym (Rehovot), C. Foias (Col
lege Station), J. W. Helton (Vice-President, La Jolla), M. A. Kaashoek (Vice
President, Amsterdam), H. Langer (Vienna), R. Mennicken (Regensburg), L. Rod
man (Williamsburg), J. G. Stampfli (Bloomington).
The purpose of IWOTA is to bring together mathematicians and engineers
interested in operator theory and its applications to related fields, from differential
equations, harmonic and complex analysis, to mathematical systems and control
theory and signal processing. In fact, every two years IWOTA gathers leading
experts from over the world for an intensive exchange of information and opinions,
and for tracing the future developments in the field. The large participation of
researchers from Eastern European and CIS countries is also an important feature
of IWOTA meetings.
The program of IWOTA-2000 consisted of 17 plenary lectures of 50 minutes
including 5 minutes for questions and remarks, and 90 section lectures of 45 and 30
minutes also including 5 minutes for questions and remarks. There were more than
170 registered participants from 29 countries of all continents (except Antarctica):
Argentina - 1, Armenia - 1, Austria - 1, Azerbaijan - 1, Canada- 1, Finland - 4,
France - 37, Germany - 5, Hungary - 1, Iran - 1, Israel - 14, Japan - 1, Maroc -
2, Mexico - 1, The Netherlands - 6, New Zealand - 2, Norway 2, Poland - 3,
Portugal - 2, Romania - 6, Russia - 10, Spain - 3, Sweden - 2, TUrkey - 1,
Ukraine - 20, United Kingdom - 4, USA - 32, Uzbekistan - 1, Venezuela - 4. The
list of participants is given below.
Some financial support was provided for some participants, especially from
the Eastern countries. This has been made possible through the generous sponsor
ing by international and French institutions listed below. We are very grateful for
their help.
viii
Special thanks. We thank the City of Bordeaux for the welcome reception on
Thesday, June 13. Warmest thanks are given to an informal team of our closest
collaborators working hard for this large meeting: Genevieve Castaignede, Em
manuel Fricain, Stanislav Kupin, Cathy Metivier, Ludmila Nikolskaia, and Pascale
Vitse, as well as to many others whose timely advice was so important, namely to
Eric Amar, Hakim Bachir, Robert Deville, Iban Harlouchet, Andreas Hartmann,
Chantal Menini, Macha Nikolskaia, David Sherman, Elisabeth Strouse, and Fouad
Zarouf.
Acknowledgements. As the majority of its homologues, the IWOTA confer
ences have no permanent funding. Their existence and function rely on financial aid
from international and national organizations supporting the development of fun
damental sciences. We gratefully acknowledge the following for their financial sup
port: INTAS (International Association for the Promotion of Cooperation with Sci
entists from the Independent States of the former Soviet Union), European Union;
Ministere de l'Education Nationale, de la Recherche et de la Technologie, France;
INRIA (Institut National de Recherche en Informatique et en Automatique, Sophia
Antipolis), France; CNRS (Centre National de Recherche Scientifique), France;
Ministere des Affaires Etrangeres, France; Region Aquitaine; Universite Bordeaux
I; Universite Lyon I; Universite Lille I; Laboratoire de Mathematiques Pures de
Bordeaux; Institut de Mathematiques de Bordeaux; Ville de Bordeaux.
Organizing Committee: Prof. Nikolai Nikolski (Chairman, Universite
Bordeaux-I), Prof. Laurent Baratchart (INRIA, Sophia Antipolis), Dr. Alexander
Borichev (Universite Bordeaux I), Dr. Gilles Cassier (Universite Lyon I), Prof.
Jean Esterle (Universite Bordeaux I), Prof. V.-H.Vasilescu (Universite Lille I)
ix
Contents
Preface. . . ... .... . .. . . . .. ... ................. . .. ..... ........ .... . .. . v
List of participants of IWOTA-2000 ................................... xi
D. Alpay, T. Ya. Azizov, A. Dijksma, H. Langer
The Schur algorithm for generalized Schur functions I:
coisometric realizations ............................................... 1
J. A. Ball, V. Vinnikov
Hardy spaces on a finite bordered Riemann surface, multivariable operator
model theory and Fourier analysis along a unimodular curve ............. 37
L. Baratchart, V. A. Prokhorov, E. B. SafI
On Hankel operators associated with Markov functions 57
M. Birman, T. Suslina
Threshold effects near the lower edge of the spectrum for periodic differential
operators of mathematical physics ..................................... 71
A. Bottcher, Yu. I. Karlovich
Cauchy's singular integral operator and its beautiful spectrum. . . . . . . . . . .. 109
I. Chalendar, J. Leblond, J. R. Partington
Approximation problems in some holomorphic spaces, with applications ... 143
L. A. Coburn
The Bargmann isometry and Gabor-Daubechies wavelet localization
operators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 169
R. Curtain, G. Weiss, M. Weiss
Stabilization of irrational transfer functions by controllers with internal loop 179
K. R. Davidson
Free Semigroup Algebras. A Survey ......... . . . . . . . . . . . . . . . . . . . . . . . . . .. 209
R. G. Douglas, G. Misra, C. Varughese
Some geometric invariants from resolutions of Hilbert modules. . . . . . . . . . .. 241
J. Eschmeier, M. Putinar
Some remarks on spherical isometries .................................. 271
S. H. Ferguson
Higher-order Hankel forms and cohomology groups ...................... 293
C. Foias, A. E. Frazho, M. A. Kaashoek
A weighted version of almost commutant lifting ......................... 311
Y. Latushkin, R. Shvydkoy
Hyperbolicity of semigroups and Fourier multipliers 341
A. V. Megretski
Relaxations of quadratic programs in operator theory and system analysis . 365
x
F. Nazarov, S. Treil, A. Volberg
Bellman function in stochastic control and harmonic analysis 393
A. G. Poltoratski
Integral representations and uniqueness sets for star-invariant subspaces 425
O. J. Statfans
Well-posed linear systems, Lax-Phillips scattering, and LP-multipliers 445
S. M. Verduyn Lunel
Spectral theory for delay equations .................................... 465
D. Yafaev
On a singular perturbation of a multiplication operator .................. 509
xi
List of Participants of IWOTA-2000
Abakumov, Evgeny, Equipe d'Analyse et de Mathematiques Appliquees, Universite de
Marne-la-Vallee, Cite Descartes - 5, Bd Descartes, Champs-sup-Marne, 77454 Marne
la-Vallee CEDEX 2, France.
Adamyan, Vadim, Department of Theoretical Physics, Odessa State University, ul. Dvo
ryanskaya 2, 270044 Odessa, Ukraine.
Alpay, Daniel, Department of Mathematics, Ben-Gurion University of the Negev, P.O.B.
653, Beer-Sheva 84105, Israel.
Akkar, Mohamed, UFR de Mathematiques, Universite Bordeaux 1, 351, cours de la
Liberation, 33405 Talence, France.
Amar, Eric, UFR de Mathematiques, Universite Bordeaux 1, 351, cours de la Liberation,
33405 Talence, France.
Ammari, Kais, Institut Elie Cartan, Departement de Mathematiques, Universite Nancy
I, 54506 Vandoeuvre-Ies-Nancy, France.
Arazy, Jonathan, Department of Mathematics, University of Haifa, Mount Carmel, Haifa
31905, Israel.
Arlinskii, Yury, East Ukrainian State University, Kvartal Molodyozhny 20-A, Lugansk
348034, Ukraine.
Arov, Damir Z., prosp. Ak. Glushko 15, kv. 18, Odessa, 270104 Ukraine.
A vdonin, Sergei, Mathematics Department, University of Tennessee, Knoxville, TN
37996-1300, USA.
Azizov, Tomas, Dept. of Math., Voronezh State University, Universitetskaya pI. 1, Voro
nezh 394693, Russia.
Bachir, Mohamed, UFR de Mathematiques, Universite Bordeaux 1, 351, cours de la
Liberation, 33405 Talence, France.
Badea, Catalin, UFR de Mathematiques, Universite des Sciences, et Technologies de Lille,
59655 Villeneuve d'Ascq Cedex, France.
Bakonyi, Mihaly, Department of Mathematics, Georgia State University, Atlanta, GA
30303, USA.
Balazard, Michel, UFR de Mathematiques, Universite Bordeaux 1, 351, cours de la
Liberation, 33405 Talence, France.
Ball, Joseph A., Department of Mathematics, Virginia Tech, Blacksburg VA 24061-0123,
USA.
Baratchart, Laurent, "Projet Miaou", INRIA, 2004, route de Lucioles BP93, 06902 Sophia
Antipolis Cedex, France.
Belishev, Mikhail I., St-Petersburg Dept. of the Steklov, Mathematical Institute (POMI),
Fontanka 27, St. Petersburg 191011, Russia.
Belitskii, Genrich, Department of Mathematics, Ben-Gurion University of the Negev,
P.O.B. 653, Beer-Sheva 84105, Israel.
Berezansky, Yurij, Institute of Mathematics, Ukrainian Acad. Sci., 3 Tereshchenkivs'ka
Str., 01601 Kyiv, Ukraine.