Nikolai K. Nikolski – författare

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.

A.N. Kolmogorov (Tambov 1903, Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject.

Each chapter treats one of Kolmogorov''s research themes, or a subject that was invented as a consequence of his discoveries. The authors present here his contributions, his methods, the perspectives he opened to us, the way in which this research has evolved up to now, along with examples of recent applications and a presentation of the modern prospects.

This book can be read by anyone with a master''s (or even a bachelor''s) degree in mathematics, computer science or physics, or more generally by anyone who likes mathematical ideas. Rather than presenting detailed proofs, the main ideas are described, and a bibliography for those who wish to understand the technical details.