Linear Operators And Their Spectra

Author : E. Brian Davies
Publisher : Cambridge University Press
Page : 436 pages
File Size : 55,7 Mb
Release : 2007-04-26
Category : Mathematics
ISBN : 9781139464338

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Linear Operators and their Spectra by E. Brian Davies Pdf

This 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.

Author : Vladimir Müller
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 40,6 Mb
Release : 2007-12-24
Category : Mathematics
ISBN : 9783764382650

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Spectral Theory of Linear Operators 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.

Author : Edward Brian Davies
Publisher : Unknown
Page : 451 pages
File Size : 49,9 Mb
Release : 2007
Category : Electronic books
ISBN : 1107170281

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Linear Operators and Their Spectra by Edward Brian Davies Pdf

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

Author : Edward Brian Davies
Publisher : Unknown
Page : 451 pages
File Size : 42,8 Mb
Release : 2007
Category : Linear operators
ISBN : 0511285795

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Linear Operators and Their Spectra by Edward Brian Davies Pdf

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

Author : Henry R. Dowson
Publisher : Unknown
Page : 444 pages
File Size : 42,6 Mb
Release : 1978
Category : Banach spaces
ISBN : UCAL:B4406582

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Spectral Theory of Linear Operators by Henry R. Dowson Pdf

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

Author : Aref Jeribi
Publisher : Springer
Page : 599 pages
File Size : 43,8 Mb
Release : 2015-07-04
Category : Science
ISBN : 9783319175669

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Spectral Theory and Applications of Linear Operators and Block Operator Matrices by Aref Jeribi Pdf

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 : Vladimir Müller
Publisher : Birkhäuser
Page : 390 pages
File Size : 47,6 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.

Author : Israel Gohberg,Seymour Goldberg
Publisher : Birkhäuser
Page : 291 pages
File Size : 51,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461259855

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Basic Operator Theory by Israel Gohberg,Seymour Goldberg Pdf

rii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators; operational calculus is next presented as a nat ural outgrowth of the spectral theory. The second part of the text concentrates on Banach spaces and linear operators acting on these spaces. It includes, for example, the three 'basic principles of linear analysis and the Riesz Fredholm theory of compact operators. Both parts contain plenty of applications. All chapters deal exclusively with linear problems, except for the last chapter which is an introduction to the theory of nonlinear operators. In addition to the standard topics in functional anal ysis, we have presented relatively recent results which appear, for example, in Chapter VII. In general, in writ ing this book, the authors were strongly influenced by re cent developments in operator theory which affected the choice of topics, proofs and exercises. One of the main features of this book is the large number of new exercises chosen to expand the reader's com prehension of the material, and to train him or her in the use of it. In the beginning portion of the book we offer a large selection of computational exercises; later, the proportion of exercises dealing with theoretical questions increases. We have, however, omitted exercises after Chap ters V, VII and XII due to the specialized nature of the subject matter.

Author : Abram Iezekiilovich Plesner
Publisher : Unknown
Page : 256 pages
File Size : 53,6 Mb
Release : 1969
Category : Mathematics
ISBN : UCAL:B4409948

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Spectral Theory of Linear Operators by Abram Iezekiilovich Plesner Pdf

Author : Aref Jeribi
Publisher : CRC Press
Page : 208 pages
File Size : 48,6 Mb
Release : 2018-04-17
Category : Mathematics
ISBN : 9781351046251

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Linear Operators and Their Essential Pseudospectra by Aref Jeribi Pdf

Linear 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 : Francoise Chatelin
Publisher : SIAM
Page : 482 pages
File Size : 49,5 Mb
Release : 2011-05-26
Category : Mathematics
ISBN : 9780898719994

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Spectral Approximation of Linear Operators by Francoise Chatelin Pdf

Originally published: New York: Academic Press, 1983.

Author : Aymen Ammar,Aref Jeribi
Publisher : CRC Press
Page : 284 pages
File Size : 46,7 Mb
Release : 2021-09-15
Category : Mathematics
ISBN : 9781000293135

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Spectral Theory of Multivalued Linear Operators by Aymen Ammar,Aref Jeribi Pdf

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 : Michael Gil'
Publisher : CRC Press
Page : 224 pages
File Size : 44,5 Mb
Release : 2017-03-03
Category : Mathematics
ISBN : 9781498796910

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Bounds for Determinants of Linear Operators and their Applications by Michael Gil' Pdf

This book deals with the determinants of linear operators in Euclidean, Hilbert and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators, enable us to describe the spectra, to evaluate the multiplicities of eigenvalues, etc. We derive upper and lower bounds, and perturbation results for determinants, and discuss applications of our theoretical results to spectrum perturbations, matrix equations, two parameter eigenvalue problems, as well as to differential, difference and functional-differential equations.

Author : Bernard Helffer
Publisher : Cambridge University Press
Page : 263 pages
File Size : 46,8 Mb
Release : 2013-01-17
Category : Mathematics
ISBN : 9781107032309

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Spectral Theory and Its Applications by Bernard Helffer Pdf

Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.

Author : Christophe Cheverry,Nicolas Raymond
Publisher : Springer Nature
Page : 258 pages
File Size : 43,5 Mb
Release : 2021-05-06
Category : Mathematics
ISBN : 9783030674625

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A Guide to Spectral Theory by Christophe Cheverry,Nicolas Raymond Pdf

This 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.