The articles in this book are based on talks at a conference devoted to interrelations between function theory and the theory of operators. The main theme of the book is the role of Alexandrov-Clark measures. Two of the articles provide the introduction to the theory of Alexandrov-Clark measures and to its applications in the spectral theory of linear operators. The remaining articles deal with recent results in specific directions related to the theme of the book.

This volume contains the proceedings of the AMS Special Session on Recent Progress in Function Theory and Operator Theory, held virtually on April 6, 2022. Function theory is a classical subject that examines the properties of individual elements in a function space, while operator theory usually deals with concrete operators acting on such spaces or other structured collections of functions. These topics occupy a central position in analysis, with important connections to partial differential equations, spectral theory, approximation theory, and several complex variables. With the aid of certain canonical representations or “models”, the study of general operators can often be reduced to that of the operator of multiplication by one or several independent variables, acting on spaces of analytic functions or compressions of this operator to co-invariant subspaces. In this way, a detailed understanding of operators becomes connected with natural questions concerning analytic functions, such as zero sets, constructions of functions constrained by norms or interpolation, multiplicative structures granted by factorizations in spaces of analytic functions, and so forth. In many cases, non-obvious problems initially motivated by operator-theoretic considerations turn out to be interesting on their own, leading to unexpected challenges in function theory. The research papers in this volume deal with the interplay between function theory and operator theory and the way in which they influence each other.

Contains the proceedings of the International Workshop on Operator Theory and Applications (IWOTA 2006) held at Seoul National University, Seoul, Korea, from July 31 to August 3, 2006. This volume contains sixteen research papers which reflect developments in operator theory and applications.

This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.

These 35 refereed articles report on recent and original results in various areas of operator theory and connected fields, many of them strongly related to contributions of Sz.-Nagy. The scientific part of the book is preceeded by fifty pages of biographical material, including several photos.

In the modern study of Hilbert space operators there has been an increasingly subtle involvement with analytic function theory. This is evident in the analysis of subnormal operators, Toeplitz operators and Hankel operators, for example. On the other hand the operator theoretic viewpoint of interpolation by analytic functions is a powerful one. There has been significant activity in recent years, within these enriching interactions, and the time seemed right for an overview ot the main lines of development. The Advanced Study Institute 'Operators and Function Theory' in Lancaster, 1984, was devoted to this, and this book contains ex panded versions (and one contraction) of the main lecture prog ramme. These varied articles, by prominent researchers, include, for example, a survey of recent results on subnormal operators, recent work of Soviet mathematicians on Hankel and Toeplitz operators, expositions of the decomposition theory and inter polation theory for Bergman, Besov and Bloch spaces, with applic ations for special operators, the Krein space approach to inter polation problems, •• and much more. It is hoped that these proceedings will bring all this lively mathematics to a wider audience. Sincere thanks are due to the Scientific Committee of the North Atlantic Treaty Organisation for the generous support that made the institute possible, and to the London Mathematical Society and the British Council for important additional support. Warm thanks also go to Barry Johnson and the L.M.S. for early guidance, and to my colleague Graham Jameson for much organisational support.

This book is dedicated to Victor Emmanuilovich Katsnelson on the occasion of his 75th birthday and celebrates his broad mathematical interests and contributions.Victor Emmanuilovich’s mathematical career has been based mainly at the Kharkov University and the Weizmann Institute. However, it also included a one-year guest professorship at Leipzig University in 1991, which led to him establishing close research contacts with the Schur analysis group in Leipzig, a collaboration that still continues today. Reflecting these three periods in Victor Emmanuilovich's career, present and former colleagues have contributed to this book with research inspired by him and presentations on their joint work. Contributions include papers in function theory (Favorov-Golinskii, Friedland-Goldman-Yomdin, Kheifets-Yuditskii) , Schur analysis, moment problems and related topics (Boiko-Dubovoy, Dyukarev, Fritzsche-Kirstein-Mädler), extension of linear operators and linear relations (Dijksma-Langer, Hassi-de Snoo, Hassi -Wietsma) and non-commutative analysis (Ball-Bolotnikov, Cho-Jorgensen).

This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them. Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions; Bernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others. Offering a selection of the latest and most exciting results obtained by world-leading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing.

Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex variables, distributed parameter systems and control theory, mathematical physics, wavelets, and numerical analysis.