Complex Analysis, Operators, and Related Topics: The S. A. Vinogradov Memorial Volume

406 Pages·2000·9.449 MB·English

by  Victor P. Havin, Nikolai K. Nikolski (auth.), Victor P. Havin, Nikolai K. Nikolski (eds.)

Operator Theory
Advances and Applications
Vol. 113
Editor:
I. Gohberg
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Complex Analysis, Operators,
and Related Topics
The S. A. Vinogradov Memorial Volume
Victor P. Havin
Nikolai K. Nikolski
Editors
Springer Basel AG
Editors:
Victor P. Havin Nikolai K. Nikolski
Department of Mathematics Laboratoire de Mathematiques Pures
St. Petersburg University UFR de Mathematiques et Informatique
Bibliotechnaia pi. 2 Universite de Bordeaux I
198904 Stary Peterhof, St. Petersburg 351, cours de la Liberation
Russia 33405 Talence Cedex
France
1991 Mathematics Subject Classification 47-06; 32-06
A CIP catalogue record for this book is available from the
Library of Congress, Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data
Complex analysis, operators, and related topics : the S. A.
Vinogradov memorial volume / Victor P. Havin ; Nikolai K. Nikolski
ed. - Basel; Boston ; Berlin : Birkhäuser, 2000
(Operator theory ; Vol. 113)
ISBN 978-3-0348-9541-5 ISBN 978-3-0348-8378-8 (eBook)
DOI 10.1007/978-3-0348-8378-8
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© 2000 Springer Basel AG
Originally published by Birkhäuser Verlag in 2000
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A Word from the Editors
This volume contains 28 articles dedicated to the memory of Stanislav A. Vino
gradov. We also decided to include the English translations of two of Vinogradov's
articles, true jewels of the volume, we believe. Each was written for a separate pur
pose: the first was for Vinogradov's PhD ("candidate") defense (1968, Leningrad
State University) and the second for his "doctoral" defense (1983, Steklov Math
ematical Institute, Leningrad). Both articles are thesis abstracts ("Avtoreferat"
in Russian), in accordance with Russian rules of thesis defenses. Fewer than 80
copies of each were printed and the Russian originals are hardly accessible now.
They have been translated by V.Havin for this volume. Our joint introductory
article on Vinogradov's life and mathematics contains some comments and addi
tions.
We would have been unable to prepare this memorial volume without gen
erous assistance, both technical and mathematical, of our and S.A.Vinogradov's
friends and colleagues
K. Abramenko A. Aleksandrov
A. Baranov D.Belyaev
V. Chebotareva J. Choksi
E. Dyn'kin K.Dyakonov
M.Gamal V.Kapustin
P. Koosis S. Kupin
A.Lodkin A. Nersessian
V. Peller A.Petrov
A. Plotkin D.Sherman
A. Sudakov I. Verbitskii
I. Videnskii A. Volberg
We are very sorry to conclude this note with the sad news that Seva (Evsei)
Dyn'kin unexpectedly died during the preparation of this volume. He was one of
the most brilliant members of St.Petersburg Analysis Seminar and Vinogradov's
circle, a very original and strong analyst and an unforgettable personality.
Victor Havin
Nikolai Nikolski
Contents
Stanislav Aleksandrovich Vinogradov, his life and mathematics............ 1
List of publications of S.A.Vinogradov .................................... 19
B.A. Vinogradov
Interpolation problems for analytic functions continuous
in the closed disk and for functions whose sequence
of coefficients is in lP .............•.................................. 23
B.A. Vinogradov
Free interpolation in spaces of analytic functions. .. .. .. .. .. .. .. .. .. .. 31
Contributed Papers
A. B. Aleksandrov
On embedding theorems for coinvariant subspaces of
the shift operator, I .................................................. 45
K. M. Dyakonov
Continuous and compact embeddings between
star-invariant subspaces ............................................. 65
I I
E. Dyn' kin
Rational functions in Bergman spaces ................................ 77
E. Gladkova (Bhtern)
S. A. Vinogradov, as I remember him................................ 95
B. Hukovic, B. Treil, A. Volberg
The Bellman functions and sharp weighted inequalities
for square functions .................................................. 97
J.-P. Kahane
Multiplicative chaos and multimeasures .............................. 115
B. Ya. Khavinson
Some remarks to problems of approximation with prescribed rate .... 127
B. V. Kislyakov
Interpolation involving bounded bianalytic functions ................. 135
P. Koosis
Carleson's interpolation theorem deduced from a result of Pick ....... 151
viii Contents
B. Korenblum
A -a zero sets: new methods and techniques .......................... 163
A. M. Kotochigov
Interpolation sets for the Holder spaces of functions
analytic in a strip ................................................... 179
P. Ku rasov, B. Pavlov
Scattering problem with physical behavior of scattering
matrix and operator relations........................................ 195
V. V. Lebedev
Spectra of inner functions and lP-multipliers ......................... 205
E. Malinnikova
The theorem on three spheres for harmonic differential forms ........ 213
V. Maiya, T. Shaposhnikova
Traces and extensions of multipliers in pairs of Sobolev spaces ....... 221
F.L. Nazarov
Complete version of Turan's lemma for trigonometric polynomials
on the unit circumference ............................................ 239
F. L. Nazarov, A. N. Podkorytov
Ball, Haagerup, and distribution functions........................... 247
V. Oleinik
Carleson measures of Bergman spaces in domains
with nonsmooth boundary ........................................... 269
1. V. Ostrovskii
On the zeros of tails of power series .................................. 279
V. Peller
Regularity conditions for vectorial stationary processes ............... 287
M. Putinar, H. S. Shapiro
The Friedrichs operator of a planar domain .......................... 303
F. A. Shamoyan, E. N. Shubabko
Parametrical representations of some classes of holomorphic
functions in the disk ................................................. 331
S. Shimorin
Double power series and reproducing kernels ......................... 339
N. A. Shirokov
Outer functions in yet another class of analytic functions ............ 349
M. Solomyak
Estimates for the approximation numbers of the weighted
Riemann-Liouville operator in the spaces Lp ......................... 371
Contents ix
G. Ts. Thmarkin
Special transformations of Cauchy type integral spaces ............... 385
I. E. Verbitsky
A dimension-free Carleson measure inequality........................ 393
I. V. Videnskii
Carleman formula for some spaces of functions analytic
in the disk and smooth in its closure ................................. 399
Stanislav A.Vinogradov
May 1, 1941-November 14, 1997
Operator Theory:
Advances and Applications, Vol. 113
© 2000 Birkhauser Verlag BasellSwitzerland
Stanislav Aleksandrovich Vinogradov,
His Life and Mathematics
V. P. Havin and N. K. Nikolski
This volume is dedicated to the memory of Slava Vinogradov,
our dear friend. His untimely death has shaken many who knew and loved him.
Life
S.A.Vinogradov was born in Leningrad on May 1, 1941, on the eve of the German
invasion. The siege began when he was a baby of 5 months, his father Aleksandr
Antonovich fell at the front, and his mother Olga Ivanovna had to overcome inde
scribable hardships to save the child from starvation amidst artillery and aircraft
bombardments. Postwar years were also hard; her income was scarce (she was
a janitor). But she had luck with her son. People who knew him in the forties
remember his early addiction to books (mainly classical Russian literature). He
was successful at school, especially in mathematics. He joined the mathematical
circle of the Palace of Young Pioneers where many Leningrad schoolchildren de
veloped their talents under the guidance of university teachers and students. In
his last high school year Stanislav was uncertain about which of the numerous
Leningrad institutes to choose for his further education. His hesitation was over
after his visit to the mathematics department of the Leningrad State University
where G.M.Fichtenholz, a famous professor and brilliant lecturer, gave a talk for
high school students (an elementary survey of Calculus). Vinogradov stated his
decision as follows: "This is the right place for me to choose, since such people
teach here" .
He passed his entrance exams quite successfully and impressed his examiners.
Slava quickly became one of the brightest students. The first author of this preface
had him in his class and remembers Vinogradov's vivid and keen interest in the
subject (power series in the spirit of Landau's "Darstellung und Begriindung",
the Hardy classes, and other spaces of analytic functions). His reaction was always
sharp and swift. G. P. Akilov who was giving the course on Functional Analysis was
impressed by the following episode. In one of his introductory lectures he proved
that the intersection of any decreasing sequence of closed balls in a complete metric
space is non-empty if the radii tend to zero; he had then mentioned that (maybe)
the last condition is redundant. Vinogradov protested immediately, saying that
this is so in a Banach space, but not in general.