Complex Analysis, Operators, and Related Topics

Nikolai K. Nikolski

ISBN 10: 3764362146 / ISBN 13: 9783764362140

Published by Birkhäuser Basel, Birkhäuser Basel Jan 2000, 2000

About this Item

Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 424 pp. Englisch.

Seller Inventory # 9783764362140

Bibliographic Details

• Title: Complex Analysis, Operators, and Related Topics
• Publisher: Birkhäuser Basel, Birkhäuser Basel Jan 2000
• Publication Date: 2000
• Language: English
• ISBN 10: 3764362146
• ISBN 13: 9783764362140
• Binding: Buch
• Condition: Neu

About this title

Synopsis

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.

Product Description

This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. 30 carefully selected surveys and research papers are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques.