Complex analysis, operators, and related topics

This volume addresses topical problems and applications of operator theory in conjunction with modern complex analysis, featuring 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 from a holomorphic perspective; various holomorphic spaces such as Hardy, Bergman, Hölder, and Sobolev spaces; analytic functions smooth up to the boundary, exploring their properties related to Nevanlinna-Smirnov factorization, division, multiplication, and zero sets; a novel approach to weighted inequalities for singular integrals using the Bellman function; 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 alongside spectral analysis of certain differential operators. These themes are interconnected through an "operator theoretic ideology" and the application of modern function theoretical techniques. The volume honors S. A. Vinogradov, including a bibliographical note with his portrait, a survey of his mathematical contributions, and translations of two of his surveys that are now difficult to access in their original Russian.