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Complex Analysis, Operators, and Related Topics

The S. A. Vinogradov Memorial Volume

  • Victor P. Havin
  • Nikolai K. Nikolski

Part of the Operator Theory: Advances and Applications book series (OT, volume 113)

Table of contents

  1. Front Matter
    Pages i-x
  2. Stanislav Aleksandrovich Vinogradov, His Life and Mathematics

    1. Victor P. Havin, Nikolai K. Nikolski
      Pages 1-18
  3. List of Publications of S.A. Vinogradov

    1. Victor P. Havin, Nikolai K. Nikolski
      Pages 19-22
  4. Interpolation Problems for Analytic Functions Continuous in the Closed Disk and for Functions whose Sequence of Coefficients is in l p

  5. Free Interpolation in Spaces of Analytic Functions

  6. Contributed Papers

    1. Front Matter
      Pages 43-43
    2. Evsey Dyn’kin
      Pages 77-94
    3. E. Gladkova
      Pages 95-96
    4. Jean-Pierre Kahane
      Pages 115-126
    5. Boris Korenblum
      Pages 163-178
    6. V. V. Lebedev
      Pages 205-212
    7. V. Maz’ya, T. Shaposhnikova
      Pages 221-237
    8. Fedor L. Nazarov, Anatoliy N. Podkorytov
      Pages 247-267
    9. I. V. Ostrovskii
      Pages 279-285
    10. Mihai Putinar, Harold S. Shapiro
      Pages 303-330
    11. Serguei Shimorin
      Pages 339-348
    12. Genrikh Ts. Tumarkin
      Pages 385-392
    13. I. E. Verbitsky
      Pages 393-398

About these proceedings

Introduction

This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. It consists of 30 carefully selected surveys and research papers.

The main subjects of the volume include:
· free interpolation by analytic functions in its development from the pathbreaking works by L. Carleson up to the most recent achievements and in its connections with the theory of singular integral operators and Carleson-type embedding theorems, moment problems etc.
· Szökefalvi-Nagy-Foias model spaces studied from the point of view of holomorphic spaces
· holomorphic spaces (Hardy, Bergman, Hölder, and Sobolev spaces)
· analytic functions smooth up to the boundary with their subtle properties related to the Nevanlinna-Smirnov factorization, division and multiplication, and zero sets
· a new approach to weighted inequalities for singular integrals based on the Bellman function in optimization theory;
· the uncertainty principle in harmonic analysis and, in particular, a complete version of Turan‘s lemma on trigonometric sums
· Hankel operators and stationary Gaussian processes
· Fourier multipliers, and spectral analysis of some differential operators.

These themes are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques.
The book is dedicated to the memory of S. A. Vinogradov. It contains a bibliographical note (with a lively portrait) of S. A. Vinogradov, a detailed survey of his mathematical achievements, and a complete list of publications, as well as the translations of two of Vinogradov‘s surveys whose Russian originals are now hardly accessible.

Keywords

Complex analysis Nevanlinna theory Operator theory Singular integral calculus differential equation distribution harmonic analysis measure

Editors and affiliations

  • Victor P. Havin
    • 1
  • Nikolai K. Nikolski
    • 2
  1. 1.Department of MathematicsSt. Petersburg UniversityStary Peterhof, St. PetersburgRussia
  2. 2.Laboratoire de Mathématiques PuresUFR de Mathématiques et Informatique Université de Bordeaux ITalence CedexFrance

Bibliographic information

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