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Complex Analysis, Operators, and Related Topics

The S. A. Vinogradov Memorial Volume

  • Conference proceedings
  • © 2000

Overview

Editors:
  1. Victor P. Havin

    1. Department of Mathematics, St. Petersburg University, Stary Peterhof, St. Petersburg, Russia

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  2. Nikolai K. Nikolski

    1. Laboratoire de Mathématiques Pures, UFR de Mathématiques et Informatique Université de Bordeaux I, Talence Cedex, France

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

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Table of contents (32 papers)

  1. Contributed Papers

    1. Traces and Extensions of Multipliers in Pairs of Sobolev Spaces

      • V. Maz’ya, T. Shaposhnikova
      Pages 221-237

    2. Complete Version of Turan’s Lemma for Trigonometric Polynomials on the Unit Circumference

      • Fedor L. Nazarov
      Pages 239-246

    3. Ball, Haagerup, and Distribution Functions

      • Fedor L. Nazarov, Anatoliy N. Podkorytov
      Pages 247-267

    4. Carleson Measures of Bergman Spaces in Domains with Nonsmooth Boundary

      • Vladimir L. Oleinik
      Pages 269-277

    5. On the Zeros of Tails of Power Series

      • I. V. Ostrovskii
      Pages 279-285

    6. Regularity Conditions for Vectorial Stationary Processes

      • Vladimir Peller
      Pages 287-301

    7. The Friedrichs Operator of a Planar Domain

      • Mihai Putinar, Harold S. Shapiro
      Pages 303-330

    8. Parametrical Representations of Some Classes of Holomorphic Functions in the Disk

      • F. A. Shamoyan, E. N. Shubabko
      Pages 331-338

    9. Double Power Series and Reproducing Kernels

      • Serguei Shimorin
      Pages 339-348

    10. Outer Functions in yet Another Class of Analytic Functions

      • N. A. Shirokov
      Pages 349-370

    11. Estimates for the Approximation Numbers of the Weighted Riemann-Liouville Operator in the Spaces L p

      • Michael Solomyak
      Pages 371-383

    12. Special Transformations of Cauchy Type Integral Spaces

      • Genrikh Ts. Tumarkin
      Pages 385-392

    13. A Dimension-free Carleson Measure Inequality

      • I. E. Verbitsky
      Pages 393-398

    14. Carleman Formula for Some Spaces of Functions Analytic in the Disk and Smooth in its Closure

      • Il’ya Videnskii
      Pages 399-408
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, St. Petersburg University, Stary Peterhof, St. Petersburg, Russia

    Victor P. Havin

  • Laboratoire de Mathématiques Pures, UFR de Mathématiques et Informatique Université de Bordeaux I, Talence Cedex, France

    Nikolai K. Nikolski

Bibliographic Information

  • Book Title: Complex Analysis, Operators, and Related Topics

  • Book Subtitle: The S. A. Vinogradov Memorial Volume

  • Editors: Victor P. Havin, Nikolai K. Nikolski

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8378-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2000

  • Hardcover ISBN: 978-3-7643-6214-0Published: 01 January 2000

  • Softcover ISBN: 978-3-0348-9541-5Published: 23 October 2012

  • eBook ISBN: 978-3-0348-8378-8Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: X, 408

  • Topics: Analysis

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