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

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.

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Content:
Front Matter....Pages i-x
Stanislav Aleksandrovich Vinogradov, His Life and Mathematics....Pages 1-18
List of Publications of S.A. Vinogradov....Pages 19-22
Free Interpolation in Spaces of Analytic Functions....Pages 23-29
Front Matter....Pages 31-42
On Embedding Theorems for Coinvariant Subspaces of the Shift Operator. I....Pages 43-43
Continuous and Compact Embeddings Between Star-invariant Subspaces....Pages 45-64
Rational Functions in Bergman Spaces....Pages 65-76
S. A. Vinogradov, As I Remember Him....Pages 77-94
The Bellman Functions and Sharp Weighted Inequalities for Square Functions....Pages 95-96
Multiplicative Chaos and Multimeasures....Pages 97-113
Some Remarks to Problems of Approximation with Prescribed Rate....Pages 115-126
Interpolation Involving Bounded Bianalytic Functions....Pages 127-133
Carleson’s Interpolation Theorem Deduced from a Result of Pick....Pages 135-149
Interpolation Sets for the H?lder Spaces of Functions Analytic in a Strip....Pages 151-162
Scattering Problem with Physical Behavior of Scattering Matrix and Operator Relations....Pages 163-178
The Theorem on Three Spheres for Harmonic Differential Forms....Pages 179-194
Traces and Extensions of Multipliers in Pairs of Sobolev Spaces....Pages 195-204
Complete Version of Turan’s Lemma for Trigonometric Polynomials on the Unit Circumference....Pages 205-212
Front Matter....Pages 213-220
Ball, Haagerup, and Distribution Functions....Pages 221-237
Carleson Measures of Bergman Spaces in Domains with Nonsmooth Boundary....Pages 239-246
On the Zeros of Tails of Power Series....Pages 43-43
Regularity Conditions for Vectorial Stationary Processes....Pages 247-267
The Friedrichs Operator of a Planar Domain....Pages 269-277
Parametrical Representations of Some Classes of Holomorphic Functions in the Disk....Pages 279-285
Double Power Series and Reproducing Kernels....Pages 287-301
Outer Functions in yet Another Class of Analytic Functions....Pages 303-330
Special Transformations of Cauchy Type Integral Spaces....Pages 331-338
A Dimension-free Carleson Measure Inequality....Pages 339-348
Carleman Formula for Some Spaces of Functions Analytic in the Disk and Smooth in its Closure....Pages 349-370
....Pages 371-383