Problems And Recent Methods In Operator Theory
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Problems and Recent Methods in Operator Theory
Author: Fernanda Botelho
language: en
Publisher: American Mathematical Soc.
Release Date: 2017-04-18
This volume contains the proceedings of the Workshop on Problems and Recent Methods in Operator Theory, held at the University of Memphis, Memphis, TN, from October 15–16, 2015 and the AMS Special Session on Advances in Operator Theory and Applications, in Memory of James Jamison, held at the University of Memphis, Memphis, TN, from October 17–18, 2015. Operator theory is at the root of several branches of mathematics and offers a broad range of challenging and interesting research problems. It also provides powerful tools for the development of other areas of science including quantum theory, physics and mechanics. Isometries have applications in solid-state physics. Hermitian operators play an integral role in quantum mechanics very much due to their “nice” spectral properties. These powerful connections demonstrate the impact of operator theory in various branches of science. The articles in this volume address recent problems and research advances in operator theory. Highlighted topics include spectral, structural and geometric properties of special types of operators on Banach spaces, with emphasis on isometries, weighted composition operators, multi-circular projections on function spaces, as well as vector valued function spaces and spaces of analytic functions. This volume gives a succinct overview of state-of-the-art techniques from operator theory as well as applications to classical problems and long-standing open questions.
Recent Advances in Operator Theory
This volume contains a selection of papers in modern operator theory and its applications. Most of them are directly related to lectures presented at the Inter national Workshop on Operator Theory and its Applications held at the University of Groningen (IWOTA-98) in Groningen, the Netherlands, from June 30-July 3, 1998. The workshop was attended by 97 mathematicians-of which 12 were PhD or postdoctoral students-from 19 countries. The program consisted of 19 plenary lectures of 40 minutes and 72 lectures of 30 minutes in 4 parallell sessions. The present volume reflects the wide range and rich variety of topics presented and discussed at the workshop. The papers deal with operator polynomials and analytic operator functions, with spectral problems of (partial) differential oper ators and related operator matrices, with interpolation, completion and extension problems, with commutant lifting and dilation, with Ricatti equations and real ization problems, with scattering theory, with problems from harmonic analysis, and with topics in the theory of reproducing kernel spaces and of spaces with an indefinite metric. All papers underwent the usual refereeing process.
Recent Progress in Function Theory and Operator Theory
Author: Alberto A. Condori
language: en
Publisher: American Mathematical Society
Release Date: 2024-04-30
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.