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Author : Francoise Chatelin
Publisher : SIAM
ISBN 13 : 0898719992
Total Pages : 482 pages
Book Rating : 4.8/5 (987 download)
Download or read book Spectral Approximation of Linear Operators written by Francoise Chatelin and published by SIAM. This book was released on 2011-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Academic Press, 1983.
Author :
Publisher :
ISBN 13 :
Total Pages : 222 pages
Book Rating : 4.:/5 (918 download)
Download or read book Spectral Approximation for Linear Operators and Applications written by and published by . This book was released on 2014 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Aref Jeribi
Publisher : Springer
ISBN 13 : 3319175661
Total Pages : 608 pages
Book Rating : 4.3/5 (191 download)
Download or read book Spectral Theory and Applications of Linear Operators and Block Operator Matrices written by Aref Jeribi and published by Springer. This book was released on 2015-07-04 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Wen-so Lo
Publisher :
ISBN 13 :
Total Pages : 108 pages
Book Rating : 4.:/5 (11 download)
Download or read book Spectral Approximation Theory for Bounded Linear Operators written by Wen-so Lo and published by . This book was released on 1972 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 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 : Vladimir Müller
Publisher : Birkhäuser
ISBN 13 : 3034877889
Total Pages : 390 pages
Book Rating : 4.0/5 (348 download)
Download or read book Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras written by Vladimir Müller and published by Birkhäuser. This book was released on 2013-11-11 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Henry R. Dowson
Publisher :
ISBN 13 :
Total Pages : 444 pages
Book Rating : 4.:/5 (44 download)
Download or read book Spectral Theory of Linear Operators written by Henry R. Dowson and published by . This book was released on 1978 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: General spectral theory; Riesz operators; Hermitian operators; Prespectral operators; Well-bounded operators.
Author : Abram Iezekiilovich Plesner
Publisher :
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.3/5 (91 download)
Download or read book Spectral Theory of Linear Operators written by Abram Iezekiilovich Plesner and published by . This book was released on 1969 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : C. W. Groetsch
Publisher : Springer Science & Business Media
ISBN 13 : 3540399429
Total Pages : 134 pages
Book Rating : 4.5/5 (43 download)
Download or read book Stable Approximate Evaluation of Unbounded Operators written by C. W. Groetsch and published by Springer Science & Business Media. This book was released on 2007 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral 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.
Author : E. Brian Davies
Publisher : Cambridge University Press
ISBN 13 : 1139464337
Total Pages : 436 pages
Book Rating : 4.1/5 (394 download)
Download or read book Linear Operators and their Spectra written by E. Brian Davies and published by Cambridge University Press. This book was released on 2007-04-26 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Aymen Ammar
Publisher : CRC Press
ISBN 13 : 1000293130
Total Pages : 284 pages
Book Rating : 4.0/5 (2 download)
Download or read book Spectral Theory of Multivalued Linear Operators written by Aymen Ammar and published by CRC Press. This book was released on 2021-09-15 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : M. Thamban Nair
Publisher : World Scientific
ISBN 13 : 9812835652
Total Pages : 264 pages
Book Rating : 4.8/5 (128 download)
Download or read book Linear Operator Equations written by M. Thamban Nair and published by World Scientific. This book was released on 2009 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be. This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Author : Christophe Cheverry
Publisher : Springer Nature
ISBN 13 : 3030674622
Total Pages : 258 pages
Book Rating : 4.0/5 (36 download)
Download or read book A Guide to Spectral Theory written by Christophe Cheverry and published by Springer Nature. This book was released on 2021-05-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Nelson Dunford
Publisher :
ISBN 13 : 9780471226390
Total Pages : 696 pages
Book Rating : 4.2/5 (263 download)
Download or read book Linear Operators written by Nelson Dunford and published by . This book was released on 1963 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Israel Gohberg
Publisher : Birkhäuser
ISBN 13 : 3034879806
Total Pages : 428 pages
Book Rating : 4.0/5 (348 download)
Download or read book Basic Classes of Linear Operators written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
Author : Radu Paltanea
Publisher : Springer Science & Business Media
ISBN 13 : 1461220580
Total Pages : 208 pages
Book Rating : 4.4/5 (612 download)
Download or read book Approximation Theory Using Positive Linear Operators written by Radu Paltanea and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an examination of the multivariate approximation case Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators Many general estimates, leaving room for future applications (e.g. the B-spline case) Extensions to approximation operators acting on spaces of vector functions Historical perspective in the form of previous significant results
Author : Seymour Goldberg
Publisher :
ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.4/5 (91 download)
Download or read book Basic Operator Theory written by Seymour Goldberg and published by . This book was released on 1981 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Operator Theory provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential and integral equations, approximation theory, and numerical analysis. A textbook designed for senior undergraduate and graduate students, Basic Operator Theory begins with the geometry of Hilbert space and proceeds to the spectral theory for compact self-adjoint operators with a wide range of applications. Part of the volume is devoted to Banach spaces and operators acting on these spaces. Presented as a natural continuation of linear algebra, Basic Operator Theory provides a firm foundation in operator theory, an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
Author : Mario Ahues
Publisher : CRC Press
ISBN 13 : 1420035827
Total Pages : 401 pages
Book Rating : 4.4/5 (2 download)
Download or read book Spectral Computations for Bounded Operators written by Mario Ahues and published by CRC Press. This book was released on 2001-02-26 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact eigenvalues, eigenvectors, and principal vectors of operators with infinite dimensional ranges can rarely be found. Therefore, one must approximate such operators by finite rank operators, then solve the original eigenvalue problem approximately. Serving as both an outstanding text for graduate students and as a source of current results for
