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 concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.

This book gathers contributions written by Daniel Alpay’s friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay’s 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay’s primary research interests. The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.

A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.

This book is the second of a two volume series. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book features fully-refereed, high-quality papers exploring new results and trends in weighted norm inequalities, Schur-Agler class functions, complex analysis, dynamical systems, and dyadic harmonic analysis. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. A survey of the two weight problem for the Hilbert transform and an expository article on the Clark model to the case of non-singular measures and applications to the study of rank-one perturbations are included. The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6,2014. During the event, participants honored the memory of Cora Sadosky—a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional scientist and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.

This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.

Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.

This volume presents a set of papers based on the proceedings of the NATO Advanced Research Workshop on Multisensor Fusion for Computer Vision, held in Grenoble, France, in June 1989. The workshop focused on the fusion or integration of sensor information to achieve the optimum interpretation of a scene. The papers cover a broad range of topics, including principles and issues in multisensor fusion, information fusion for navigation, multisensor fusion for object recognition, network approaches to multisensor fusion, computer architectures for multisensor fusion, and applications of multisensor fusion. The authors have documented their own research and, in so doing,have presented the state of the art in the field. Each author is a recognized leader in his or her area in the academic, governmental, or industrial research community. Several contributors present novel points of view on the integration of information. The book gives a representative picture of current progress in multisensor fusion for computer vision among the leading research groups in Europe and North America.