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Recent Progress in Function Theory and Operator Theory

Recent Progress in Function Theory and Operator Theory PDF Author: Alberto A. Condori
Publisher: American Mathematical Society
ISBN: 1470472465
Category : Mathematics
Languages : en
Pages : 226

Book Description
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.

Recent Progress in Function Theory and Operator Theory

Recent Progress in Function Theory and Operator Theory PDF Author: Alberto A. Condori
Publisher: American Mathematical Society
ISBN: 1470472465
Category : Mathematics
Languages : en
Pages : 226

Book Description
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.

Recent Progress in Operator Theory

Recent Progress in Operator Theory PDF Author: Israel C. Gohberg
Publisher: Birkhäuser
ISBN: 3034887930
Category : Mathematics
Languages : en
Pages : 292

Book Description
This volume brings readers up to date on different aspects of operator theory and its applications, including mathematical physics, hydrodynamics, magnetohydrodynamics, quantum mechanics, astrophysics as well as the theory of networks and systems. Of practical use to a wide readership in pure and applied mathematics, physics and engineering sciences.

Recent Advances in Operator-Related Function Theory

Recent Advances in Operator-Related Function Theory PDF Author: Alec L. Matheson
Publisher: American Mathematical Soc.
ISBN: 082183925X
Category : Mathematics
Languages : en
Pages : 230

Book Description
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.

Recent Developments in Nonlocal Theory

Recent Developments in Nonlocal Theory PDF Author: Giampiero Palatucci
Publisher: De Gruyter Open
ISBN: 9783110571554
Category : Mathematics
Languages : en
Pages : 450

Book Description
This edited volume aims at giving an overview of recent advances in the theory and applications of Partial Differential Equations and energy functionals related to the fractional Laplacian operator as well as to more general integro-differential operators with singular kernel of fractional differentiability. After being investigated firstly in Potential Theory and Harmonic Analysis, fractional operators defined via singular integral are nowadays riveting great attention in different research fields related to Partial Differential Equations with nonlocal terms, since they naturally arise in many different contexts, as for instance, dislocations in crystals, nonlocal minimal surfaces, the obstacle problem, the fractional Yamabe problem, and many others. Much progress has been made during the last years, and this edited volume presents a valuable update to a wide community interested in these topics. List of contributors Claudia Bucur, Zhen-Qing Chen, Francesca Da Lio, Donatella Danielli, Serena Dipierro, Rupert L. Frank, Maria del Mar Gonzalez, Moritz Kassmann, Tuomo Kuusi, Giuseppe Mingione, Giovanni Molica Bisci, Stefania Patrizi, Xavier Ros-Oton, Sandro Salsa, Yannick Sire, Enrico Valdinoci, Xicheng Zhang.

Catherine Beneteau, Alberto A. Condori, Constanze Liaw, William T. Ross, and Alan A. Sola

Catherine Beneteau, Alberto A. Condori, Constanze Liaw, William T. Ross, and Alan A. Sola PDF Author: Catherine Bénéteau:
Publisher: American Mathematical Soc.
ISBN: 1470423057
Category : Mathematics
Languages : en
Pages : 230

Book Description
This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29–July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden. The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures. This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.

Topics in Operator Theory

Topics in Operator Theory PDF Author: Carl M. Pearcy
Publisher: American Mathematical Soc.
ISBN: 082181513X
Category : Mathematics
Languages : en
Pages : 254

Book Description
Deals with various aspects of the theory of bounded linear operators on Hilbert space. This book offers information on weighted shift operators with scalar weights.

Operator Theory, Operator Algebras, and Applications

Operator Theory, Operator Algebras, and Applications PDF Author: Deguang Han
Publisher: American Mathematical Soc.
ISBN: 0821839233
Category : Mathematics
Languages : en
Pages : 440

Book Description
This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.

Perturbation theory for linear operators

Perturbation theory for linear operators PDF Author: Tosio Kato
Publisher: Springer Science & Business Media
ISBN: 3662126788
Category : Mathematics
Languages : en
Pages : 610

Book Description


Recent Developments in Theoretical Fluid Mechanics

Recent Developments in Theoretical Fluid Mechanics PDF Author: G P Galdi
Publisher: CRC Press
ISBN: 1000941019
Category : Mathematics
Languages : en
Pages : 176

Book Description
Including previously unpublished, original research material, this comprehensive book analyses topics of fundamental importance in theoretical fluid mechanics. The five papers appearing in this volume are centred around the mathematical theory of the Navier-Stokes equations (incompressible and compressible) and certain selected non-Newtonian modifications.

Higher Structures in Topology, Geometry, and Physics

Higher Structures in Topology, Geometry, and Physics PDF Author: Ralph M. Kaufmann
Publisher: American Mathematical Society
ISBN: 1470471426
Category : Mathematics
Languages : en
Pages : 332

Book Description
This volume contains the proceedings of the AMS Special Session on Higher Structures in Topology, Geometry, and Physics, held virtually on March 26–27, 2022. The articles give a snapshot survey of the current topics surrounding the mathematical formulation of field theories. There is an intricate interplay between geometry, topology, and algebra which captures these theories. The hallmark are higher structures, which one can consider as the secondary algebraic or geometric background on which the theories are formulated. The higher structures considered in the volume are generalizations of operads, models for conformal field theories, string topology, open/closed field theories, BF/BV formalism, actions on Hochschild complexes and related complexes, and their geometric and topological aspects.