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

ISBN-13: 9783764362140 / Angielski / Twarda / 2000 / 408 str.

Victor P. Havin; Nikolai K. Nikolski; V. P. Havin

Opis

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.

Spis treści

Stanislav Aleksandrovich Vinogradov, his life and mathematics.- List of publications of S.A.Vinogradov.- Interpolation problems for analytic functions continuous in the closed disk and for functions whose sequence of coefficients is inlp.- Free interpolation in spaces of analytic functions.- Contributed Papers.- On embedding theorems for coinvariant subspaces of the shift operator, I.- Continuous and compact embeddings between star-invariant subspaces.- Rational functions in Bergman spaces.- S. A. Vinogradov, as I remember him.- The Bellman functions and sharp weighted inequalities for square functions.- Multiplicative chaos and multimeasures.- Some remarks to problems of approximation with prescribed rate.- Interpolation involving bounded bianalytic functions.- Carleson’s interpolation theorem deduced from a result of Pick.- A–?zero sets: new methods and techniques.- Interpolation sets for the Hölder spaces of functions analytic in a strip.- Scattering problem with physical behavior of scattering matrix and operator relations.- Spectra of inner functions andlp-multipliers.- The theorem on three spheres for harmonic differential forms.- Traces and extensions of multipliers in pairs of Sobolev spaces.- Complete version of Turan’s lemma for trigonometric polynomials on the unit circumference.- Ball, Haagerup, and distribution functions.- Carleson measures of Bergman spaces in domains with nonsmooth boundary.- On the zeros of tails of power series.- Regularity conditions for vectorial stationary processes.- The Friedrichs operator of a planar domain.- Parametrical representations of some classes of holomorphic functions in the disk.- Double power series and reproducing kernels.- Outer functions in yet another class of analytic functions.- Estimates for the approximation numbers of the weighted Riemann-Liouville operator in the spacesLp.- Special transformations of Cauchy type integral spaces.- A dimension-free Carleson measure inequality.- Carleman formula for some spaces of functions analytic in the disk and smooth in its closure.