Complex Analysis, Operators, and Related Topics

Mehr zum Buch

This volume addresses topical problems and applications of operator theory alongside modern complex analysis, comprising 30 selected surveys and research papers. Key subjects include: free interpolation by analytic functions, tracing its evolution from L. Carleson's foundational work to recent advancements, and its links to singular integral operators and Carleson-type embedding theorems; Szökefalvi-Nagy-Foias model spaces viewed through the lens of holomorphic spaces; various holomorphic spaces such as Hardy, Bergman, Hölder, and Sobolev spaces; the properties of analytic functions smooth up to the boundary, particularly regarding Nevanlinna-Smirnov factorization, division, multiplication, and zero sets; a novel approach to weighted inequalities for singular integrals using the Bellman function from optimization theory; the uncertainty principle in harmonic analysis, including a complete version of Turan's lemma on trigonometric sums; Hankel operators and stationary Gaussian processes; and Fourier multipliers along with the spectral analysis of certain differential operators. These themes are interconnected by an "operator theoretic ideology" and the application of modern function theoretical techniques. The volume is dedicated to the memory of S. A. Vinogradov, featuring a bibliographical note, a survey of his mathematical contributions, and translations of two of his surveys that are now difficult to access.