Spectral Decompositions And Analytic Sheaves

Author : Jörg Eschmeier,Mihai Putinar
Publisher : Oxford University Press
Page : 378 pages
File Size : 41,5 Mb
Release : 1996
Category : Language Arts & Disciplines
ISBN : 0198536674

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Spectral Decompositions and Analytic Sheaves by Jörg Eschmeier,Mihai Putinar Pdf

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 : I. Erdelyi,R. Lange
Publisher : Lecture Notes in Mathematics
Page : 138 pages
File Size : 50,6 Mb
Release : 1977-11
Category : Mathematics
ISBN : STANFORD:36105031838753

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Spectral Decompositions on Banach Spaces by I. Erdelyi,R. Lange Pdf

Author : Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar
Publisher : Springer Nature
Page : 893 pages
File Size : 43,9 Mb
Release : 2024-01-22
Category : Mathematics
ISBN : 9783031505355

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Multivariable Operator Theory by Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar Pdf

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
Page : 452 pages
File Size : 43,9 Mb
Release : 2007-05-08
Category : Mathematics
ISBN : 9781402025259

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Fredholm and Local Spectral Theory, with Applications to Multipliers by Pietro Aiena Pdf

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 : Александр Яковлевич Хелемский
Publisher : American Mathematical Soc.
Page : 496 pages
File Size : 47,6 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 0821889699

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Lectures and Exercises on Functional Analysis by Александр Яковлевич Хелемский Pdf

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
Page : 196 pages
File Size : 42,9 Mb
Release : 2004-05-13
Category : Computers
ISBN : 3540219234

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Spectral Properties of Noncommuting Operators by Brian Jefferies Pdf

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 : Krzysztof Jarosz
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 43,6 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809396

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Function Spaces by Krzysztof Jarosz Pdf

This proceedings volume presents 36 papers given by leading experts during the Third Conference on Function Spaces held at Southern Illinois University at Edwardsville. A wide range of topics in the subject area are covered. Most papers are written for nonexperts, so the book can serve as a good introduction to the topic for those interested in this area. The book presents the following broad range of topics, including spaces and algebras of analytic functions of one and of many variables, $Lp$ spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces and related subjects. Known results, open problems, and new discoveries are featured. At the time of publication, information about the book, the conference, and a list and pictures of contributors are available on the Web at www.siue.edu/MATH/conference.htm.

Author : Laura Ann Smithies
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 47,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821827253

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Equivariant Analytic Localization of Group Representations by Laura Ann Smithies Pdf

The problem of producing geometric constructions of the linear representations of a real connected semisimple Lie group with finite center, $G_0$, has been of great interest to representation theorists for many years now. A classical construction of this type is the Borel-Weil theorem, which exhibits each finite dimensional irreducible representation of $G_0$ as the space of global sections of a certain line bundle on the flag variety $X$ of the complexified Lie algebra $\mathfrak g$ of $G_0$.In 1990, Henryk Hecht and Joseph Taylor introduced a technique called analytic localization which vastly generalized the Borel-Weil theorem. Their method is similar in spirit to Beilinson and Bernstein's algebraic localization method, but it applies to $G_0$ representations themselves, instead of to their underlying Harish-Chandra modules. For technical reasons, the equivalence of categories implied by the analytic localization method is not as strong as it could be. In this paper, a refinement of the Hecht-Taylor method, called equivariant analytic localization, is developed. The technical advantages that equivariant analytic localization has over (non-equivariant) analytic localization are discussed and applications are indicated.

Author : K. B. Laursen,Michael Neumann
Publisher : Oxford University Press
Page : 610 pages
File Size : 54,5 Mb
Release : 2000
Category : Mathematics
ISBN : 0198523815

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An Introduction to Local Spectral Theory by K. B. Laursen,Michael Neumann Pdf

Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.

Author : Qazi Ibadur Rahman,Gerhard Schmeisser
Publisher : Oxford University Press
Page : 760 pages
File Size : 52,8 Mb
Release : 2002
Category : Language Arts & Disciplines
ISBN : 0198534930

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Analytic Theory of Polynomials by Qazi Ibadur Rahman,Gerhard Schmeisser Pdf

Presents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications

Author : Jim Agler,John Edward McCarthy,Nicholas John Young
Publisher : Cambridge University Press
Page : 393 pages
File Size : 51,9 Mb
Release : 2020-03-26
Category : Mathematics
ISBN : 9781108485449

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Operator Analysis by Jim Agler,John Edward McCarthy,Nicholas John Young Pdf

This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.

Author : Donald G. Babbitt,Jane E. Kister
Publisher : American Mathematical Soc.
Page : 762 pages
File Size : 54,8 Mb
Release : 2000-05-05
Category : Mathematics
ISBN : 0821896709

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Featured Reviews in Mathematical Reviews 1997-1999 by Donald G. Babbitt,Jane E. Kister Pdf

This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Author : Bernhelm Booss
Publisher : World Scientific
Page : 553 pages
File Size : 41,5 Mb
Release : 2006
Category : Science
ISBN : 9789812568052

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Analysis, Geometry and Topology of Elliptic Operators by Bernhelm Booss Pdf

Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics.The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski's work in the theory of elliptic operators.

Author : Dumitru Gaspar,Israel Gohberg,Dan Timotin,Florian H. Vasilescu,Laszlo Zsido
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 48,5 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783764373146

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Recent Advances in Operator Theory, Operator Algebras, and their Applications by Dumitru Gaspar,Israel Gohberg,Dan Timotin,Florian H. Vasilescu,Laszlo Zsido Pdf

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.

Author : Vladimir Müller
Publisher : Birkhäuser
Page : 390 pages
File Size : 50,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783034877886

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Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras by Vladimir Müller Pdf

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.