[PDF] Spectral Theory Of Multivalued Linear Operators eBook

Author : Aymen Ammar
Publisher : CRC Press
Page : 284 pages
File Size : 35,47 MB
Release : 2021-09-15
Category : Mathematics
ISBN : 1000293130

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The concept of multivalued linear operators—or linear relations—is the one of the most exciting and influential fields of research in modern mathematics. Applications of this theory can be found in economic theory, noncooperative games, artificial intelligence, medicine, and more. This new book focuses on the theory of linear relations, responding to the lack of resources exclusively dealing with the spectral theory of multivalued linear operators. The subject of this book is the study of linear relations over real or complex Banach spaces. The main purposes are the definitions and characterization of different kinds of spectra and extending the notions of spectra that are considered for the usual one single-valued operator bounded or not bounded. The volume introduces the theory of pseudospectra of multivalued linear operators. The main topics include demicompact linear relations, essential spectra of linear relation, pseudospectra, and essential pseudospectra of linear relations. The volume will be very useful for researchers since it represents not only a collection of a previously heterogeneous material but is also an innovation through several extensions. Beginning graduate students who wish to enter the field of spectral theory of multivalued linear operators will benefit from the material covered, and expert readers will also find sources of inspiration.

Author : Henry R. Dowson
Publisher :
Page : 444 pages
File Size : 50,2 MB
Release : 1978
Category : Banach spaces
ISBN :

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General spectral theory; Riesz operators; Hermitian operators; Prespectral operators; Well-bounded operators.

Author : Ronald Cross
Publisher : CRC Press
Page : 356 pages
File Size : 33,37 MB
Release : 1998-07-09
Category : Mathematics
ISBN : 9780824702199

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Constructs a theoretical framework for the study of linear relations and provides underlying concepts, rules, formulae, theorems and techniques. The book compares the inversion, adjoints, completion and closure of various classes of linear operators. It highlights compact and precompact relations.

Author : Jürgen Appell
Publisher : Walter de Gruyter
Page : 421 pages
File Size : 50,16 MB
Release : 2008-08-22
Category : Mathematics
ISBN : 3110199262

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In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The first chapter briefly recalls the definition and properties of the spectrum and several subspectra for bounded linear operators. Then some numerical characteristics for nonlinear operators are introduced which are useful for describing those classes of operators for which there exists a spectral theory. Since spectral values are closely related to solvability results for operator equations, various conditions for the local or global invertibility of a nonlinear operator are collected in the third chapter. The following two chapters are concerned with spectra for certain classes of continuous, Lipschitz continuous, or differentiable operators. These spectra, however, simply adapt the corresponding definitions from the linear theory which somehow restricts their applicability. Other spectra which are defined in a completely different way, but seem to have useful applications, are defined and studied in the following four chapters. The remaining three chapters are more application-oriented and deal with nonlinear eigenvalue problems, numerical ranges, and selected applications to nonlinear problems. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.

Author : Vladimir Müller
Publisher : Birkhäuser
Page : 390 pages
File Size : 12,73 MB
Release : 2013-11-11
Category : Mathematics
ISBN : 3034877889

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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 : Francoise Chatelin
Publisher : SIAM
Page : 482 pages
File Size : 39,85 MB
Release : 2011-05-26
Category : Mathematics
ISBN : 0898719992

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Originally published: New York: Academic Press, 1983.

Author : Aref Jeribi
Publisher : Springer
Page : 608 pages
File Size : 48,33 MB
Release : 2015-07-04
Category : Science
ISBN : 3319175661

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Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.

Author : Edward Brian Davies
Publisher :
Page : 451 pages
File Size : 13,33 MB
Release : 2007
Category : Linear operators
ISBN : 9780511285790

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Authoritative text presenting a broad view of the spectral theory of non-self-adjoint linear operators.

Author : John Locker
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 42,98 MB
Release : 2000
Category : Mathematics
ISBN : 0821820494

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Develops the spectral theory of an nth order non-self-adjoint two- point differential operator L in the complex Hilbert space L2[0,1]. The differential operator L is determined by an nth order formal differential l and by n linearly independent boundary values B1,.,Bn. Locker first lays the foundations of the spectral theory for closed linear operators and Fredholm operators in Hilbert spaces before developing the spectral theory of the differential operator L. The book is a sequel to Functional analysis and two-point differential operators, 1986. Annotation copyrighted by Book News, Inc., Portland, OR.