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.
Read and Download eBook Full
Author: Francoise Chatelin
Publisher: SIAM
Published: 2011-05-26
Total Pages: 482
ISBN-13: 0898719992
DOWNLOAD EBOOKOriginally published: New York: Academic Press, 1983.
Author:
Publisher:
Published: 2014
Total Pages: 222
ISBN-13:
DOWNLOAD EBOOKAuthor: Vladimir Müller
Publisher: Springer Science & Business Media
Published: 2007-12-24
Total Pages: 444
ISBN-13: 3764382651
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.
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.
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.
Author: Aref Jeribi
Publisher: CRC Press
Published: 2018-04-17
Total Pages: 270
ISBN-13: 135104625X
DOWNLOAD EBOOKLinear Operators and Their Essential Pseudospectra provides a comprehensive study of spectral theory of linear operators defined on Banach spaces. The central items of interest in the volume include various essential spectra, but the author also considers some of the generalizations that have been studied. In recent years, spectral theory has witnessed an explosive development. This volume presents a survey of results concerning various types of essential spectra and pseudospectra in a unified, axiomatic way and also discusses several topics that are new but which relate to the concepts and methods emanating from the book. The main topics include essential spectra, essential pseudospectra, structured essential pseudospectra, and their relative sets. This volume will be very useful for several researchers since it represents not only a collection of previously heterogeneous material but also includes discussions of innovation through several extensions. As the spectral theory of operators is an important part of functional analysis and has numerous applications in many areas of mathematics, the author suggests that some modest prerequisites from functional analysis and operator theory should be in place to be accessible to newcomers and graduate students of mathematics.
Author: Christophe Cheverry
Publisher: Springer Nature
Published: 2021-05-06
Total Pages: 258
ISBN-13: 3030674622
DOWNLOAD EBOOKThis textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.
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.
Author: P.D. Hislop
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 331
ISBN-13: 146120741X
DOWNLOAD EBOOKThe intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.
Author: Lloyd N. Trefethen
Publisher: Princeton University Press
Published: 2005-08-07
Total Pages: 634
ISBN-13: 9780691119465
DOWNLOAD EBOOKPure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.