Spectral Approximation of Linear Operators
Author: Francoise Chatelin
Publisher: SIAM
Published: 2011-05-26
Total Pages: 482
ISBN-13: 0898719992
DOWNLOAD EBOOKOriginally published: New York: Academic Press, 1983.
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Spectral Approximation for Linear Operators and Applications
Author:
Publisher:
Published: 2014
Total Pages: 222
ISBN-13:
DOWNLOAD EBOOKSpectral Theory and Applications of Linear Operators and Block Operator Matrices
Author: Aref Jeribi
Publisher: Springer
Published: 2015-07-04
Total Pages: 608
ISBN-13: 3319175661
DOWNLOAD EBOOKExamining 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.
Spectral Approximation Theory for Bounded Linear Operators
Author: Wen-so Lo
Publisher:
Published: 1972
Total Pages: 108
ISBN-13:
DOWNLOAD EBOOKIn this thesis we examine the approximation theory of the eigenvalue problem of bounded linear operators defined on a Banach space, and its applications to integral and differential equations. Special cases include the degenerate kernel method, projection method, collocation method, the Galerkin method, the method of moments, and the generalized Ritz method for solving integral or differential equations. Given a bounded linear operator, a sequence of bounded linear operator approximations is assumed to converge to it in the operator norm. We examine, among other things, the perturbation of the spectrum of the given operator; criteria for the existence and convergence of approximate eigenvectors and generalized eigenvectors; relations between the dimensions of the eigenmanifolds and generalized eigenmanifolds of the operator and those of the approximate operators.
Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras
Author: Vladimir Müller
Publisher: Birkhäuser
Published: 2013-11-11
Total Pages: 390
ISBN-13: 3034877889
DOWNLOAD EBOOKThis 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.
Spectral Theory of Linear Operators
Author: Henry R. Dowson
Publisher:
Published: 1978
Total Pages: 444
ISBN-13:
DOWNLOAD EBOOKGeneral spectral theory; Riesz operators; Hermitian operators; Prespectral operators; Well-bounded operators.
Spectral Theory of Linear Operators
Author: Abram Iezekiilovich Plesner
Publisher:
Published: 1969
Total Pages: 256
ISBN-13:
DOWNLOAD EBOOKLinear Operators and their Spectra
Author: E. Brian Davies
Publisher: Cambridge University Press
Published: 2007-04-26
Total Pages: 436
ISBN-13: 1139464337
DOWNLOAD EBOOKThis wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-self-adjoint harmonic oscillator.
Stable Approximate Evaluation of Unbounded Operators
Author: C. W. Groetsch
Publisher: Springer Science & Business Media
Published: 2007
Total Pages: 134
ISBN-13: 3540399429
DOWNLOAD EBOOKSpectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.
Spectral Theory of Multivalued Linear Operators
Author: Aymen Ammar
Publisher: CRC Press
Published: 2021-09-15
Total Pages: 284
ISBN-13: 1000293130
DOWNLOAD EBOOKThe 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.
