Analytic Functional Calculus and Spectral Decompositions PDF Download

Author: Florian-Horia Vasilescu
Publisher: Springer Science & Business Media
ISBN: 9789027713766
Category : Mathematics
Languages : en
Pages : 398

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Author: Jörg Eschmeier
Publisher: Oxford University Press
ISBN: 9780198536673
Category : Language Arts & Disciplines
Languages : en
Pages : 378

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Book Description
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: Ridgley Lange
Publisher: American Mathematical Soc.
ISBN: 082185139X
Category : Mathematics
Languages : en
Pages : 288

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Book Description
Aimed at a general mathematical audience, this book provides a careful exposition of developments in the theory of spectral decomposition. Bringing the reader from the basics up to the level of current research in the area at the time of writing, Lange and Wang present an accessible account of the techniques used in the theory and applications of decomposable operators and related classes of operators. The book begins with a discussion of criteria for decomposable and related types of operators, and an analysis that relates and distinguishes among them. Perturbation theory of decomposable and other operators, applications to classical Hilberty space operators, quasisimilarity, and a new class of weakly decomposable operators are also discussed. The book closes with an exposition of some classical theories on invariant subspaces for subdecomposable and hyponormal operators, and a presentation of the parallel spectral theory of commuting systems.

Author: Brian R. Jefferies
Publisher: Springer
ISBN: 3540707468
Category : Mathematics
Languages : en
Pages : 187

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Book Description
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: Daniel Alpay
Publisher: Springer Nature
ISBN: 3031214609
Category : Mathematics
Languages : en
Pages : 424

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Book Description
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.

Author: Ivan N. Erdelyi
Publisher: Cambridge University Press
ISBN: 9780521313148
Category : Mathematics
Languages : en
Pages : 194

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Book Description
This book, which is almost entirely devoted to unbounded operators, gives a unified treatment of the contemporary local spectral theory for unbounded closed operators on a complex Banach space. While the main part of the book is original, necessary background materials provided. There are some completely new topics treated, such as the complete spectral duality theory with the first comprehensive proof of the predual theorem, in two different versions. Also covered are spectral resolvents of various kinds (monotomic, strongly monotonic, almost localized, analytically invariant), and spectral decompositions with respect to the identity. The book concludes with an extensive reference list, including many papers published in the People's Republic of China, here brought to the attention of Western mathematicians for the first time. Pure mathematicians, especially those working in operator theory and functional analysis, will find this book of interest.

Author: Klaus D. Bierstedt
Publisher: CRC Press
ISBN: 9780824790660
Category : Mathematics
Languages : en
Pages : 556

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Book Description
These proceedings from the Symposium on Functional Analysis explore advances in the usually separate areas of semigroups of operators and evolution equations, geometry of Banach spaces and operator ideals, and Frechet spaces with applications in partial differential equations.

Author: I. Gohberg
Publisher: Birkhäuser
ISBN: 3034854757
Category : Science
Languages : en
Pages : 277

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Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 0306483734
Category : Mathematics
Languages : en
Pages : 564

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Book Description
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: Donald G. Babbitt
Publisher: American Mathematical Soc.
ISBN: 9780821896709
Category : Mathematics
Languages : en
Pages : 762

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Book Description
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.