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Table of contents (32 papers)
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Front Matter
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Stanislav Aleksandrovich Vinogradov, His Life and Mathematics
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List of Publications of S.A. Vinogradov
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Interpolation Problems for Analytic Functions Continuous in the Closed Disk and for Functions whose Sequence of Coefficients is in l p
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Free Interpolation in Spaces of Analytic Functions
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Contributed Papers
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Front Matter
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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
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Department of Mathematics, St. Petersburg University, Stary Peterhof, St. Petersburg, Russia
Victor P. Havin
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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
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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