Spectral Decompositions And Analytic Sheaves
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Author | : Jörg Eschmeier |
Publisher | : Oxford University Press |
Total Pages | : 378 |
Release | : 1996 |
Genre | : Language Arts & Disciplines |
ISBN | : 9780198536673 |
Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, various concepts from function theory and complex analytic geometry are drawn together to give a new approach to concrete spectral computations and give insights into new developments in the spectral theory of linear operators. Classical results from cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the language of homological algebra. The advantages of this approach are illustrated by a variety of examples, unexpected applications, and conceptually new ideas that should stimulate further research among mathematicians.
Author | : Ernst Albrecht |
Publisher | : Springer Nature |
Total Pages | : 893 |
Release | : 2024-01-22 |
Genre | : Mathematics |
ISBN | : 3031505352 |
Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Author | : Pietro Aiena |
Publisher | : Springer Science & Business Media |
Total Pages | : 452 |
Release | : 2007-05-08 |
Genre | : Mathematics |
ISBN | : 1402025254 |
A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.
Author | : Vladimir Müller |
Publisher | : Birkhäuser |
Total Pages | : 390 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 3034877889 |
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. Many results appear here for the first time in a monograph.
Author | : Kehe Zhu |
Publisher | : CRC Press |
Total Pages | : 360 |
Release | : 2019-05-10 |
Genre | : Mathematics |
ISBN | : 1351045547 |
Handbook of Analytic Operator Theory thoroughly covers the subject of holomorphic function spaces and operators acting on them. The spaces covered include Bergman spaces, Hardy spaces, Fock spaces and the Drury-Averson space. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators. The volume consists of eleven articles in the general area of analytic function spaces and operators on them. Each contributor focuses on one particular topic, for example, operator theory on the Drury-Aversson space, and presents the material in the form of a survey paper which contains all the major results in the area and includes all relevant references. The overalp between this volume and existing books in the area is minimal. The material on two-variable weighted shifts by Curto, the Drury-Averson space by Fang and Xia, the Cowen-Douglas class by Misra, and operator theory on the bi-disk by Yang has never appeared in book form before. Features: The editor of the handbook is a widely known and published researcher on this topic The handbook's contributors are a who's=who of top researchers in the area The first contributed volume on these diverse topics
Author | : Michiel Hazewinkel |
Publisher | : Springer Science & Business Media |
Total Pages | : 564 |
Release | : 2007-11-23 |
Genre | : Mathematics |
ISBN | : 0306483734 |
This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Author | : Александр Яковлевич Хелемский |
Publisher | : American Mathematical Soc. |
Total Pages | : 496 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821889695 |
The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.
Author | : Brian Jefferies |
Publisher | : Springer Science & Business Media |
Total Pages | : 196 |
Release | : 2004-05-13 |
Genre | : Computers |
ISBN | : 9783540219231 |
Forming functions of operators is a basic task of many areas of linear analysis and quantum physics. Weyl’s functional calculus, initially applied to the position and momentum operators of quantum mechanics, also makes sense for finite systems of selfadjoint operators. By using the Cauchy integral formula available from Clifford analysis, the book examines how functions of a finite collection of operators can be formed when the Weyl calculus is not defined. The technique is applied to the determination of the support of the fundamental solution of a symmetric hyperbolic system of partial differential equations and to proving the boundedness of the Cauchy integral operator on a Lipschitz surface.
Author | : Raúl E. Curto |
Publisher | : American Mathematical Soc. |
Total Pages | : 396 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 0821802984 |
This is a collection of papers presented at a conference on multivariable operator theory. The articles contain contributions to a variety of areas and topics which may be viewed as forming an emerging new subject. This subject involves the study of geometric rather than topological invariants associated with the general theme of operator theory in several variables. This collection will spur further discussion among the different research groups.
Author | : H. Garth Dales |
Publisher | : Cambridge University Press |
Total Pages | : 338 |
Release | : 2003-11-13 |
Genre | : Mathematics |
ISBN | : 9780521535847 |