Algebraic Multiplicity Of Eigenvalues Of Linear Operators
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Algebraic Multiplicity Of Eigenvalues Of Linear Operators
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Author : Julián López-Gómez
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-09
Algebraic Multiplicity Of Eigenvalues Of Linear Operators written by Julián López-Gómez and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-09 with Mathematics categories.
This book brings together all available results about the theory of algebraic multiplicities. It first offers a classic course on finite-dimensional spectral theory and then presents the most general results available about the existence and uniqueness of algebraic multiplicities for real non-analytic operator matrices and families. Coverage next transfers these results from linear to nonlinear analysis.
Spectral Approximation Of Linear Operators
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Author : Francoise Chatelin
language : en
Publisher: SIAM
Release Date : 2011-05-26
Spectral Approximation Of Linear Operators written by Francoise Chatelin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-26 with Mathematics categories.
Originally published: New York: Academic Press, 1983.
Spectral Theory And Applications Of Linear Operators And Block Operator Matrices
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Author : Aref Jeribi
language : en
Publisher: Springer
Release Date : 2015-07-04
Spectral Theory And Applications Of Linear Operators And Block Operator Matrices written by Aref Jeribi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-04 with Science categories.
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.
Perturbation Theory For Linear Operators
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Author : Tosio Kato
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Perturbation Theory For Linear Operators written by Tosio Kato and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Elementary Linear Algebra
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Author : Stephen Andrilli
language : en
Publisher: Academic Press
Release Date : 2022-04-05
Elementary Linear Algebra written by Stephen Andrilli and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-05 with Mathematics categories.
Elementary Linear Algebra, Sixth Edition provides a solid introduction to both the computational and theoretical aspects of linear algebra, covering many important real-world applications, including graph theory, circuit theory, Markov chains, elementary coding theory, least-squares polynomials and least-squares solutions for inconsistent systems, differential equations, computer graphics and quadratic forms. In addition, many computational techniques in linear algebra are presented, including iterative methods for solving linear systems, LDU Decomposition, the Power Method for finding eigenvalues, QR Decomposition, and Singular Value Decomposition and its usefulness in digital imaging. - Prepares students with a thorough coverage of the fundamentals of introductory linear algebra - Presents each chapter as a coherent, organized theme, with clear explanations for each new concept - Builds a foundation for math majors in the reading and writing of elementary mathematical proofs
Spectral Theory And Differential Operators
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Author : David Eric Edmunds
language : en
Publisher: Oxford University Press
Release Date : 2018
Spectral Theory And Differential Operators written by David Eric Edmunds and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.
Elementary Operator Theory
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Author : Marat V. Markin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-04-06
Elementary Operator Theory written by Marat V. Markin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-06 with Mathematics categories.
The book is intended as a text for a one-semester graduate course in operator theory to be taught "from scratch'', not as a sequel to a functional analysis course, with the basics of the spectral theory of linear operators taking the center stage. The book consists of six chapters and appendix, with the material flowing from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), the Banach Fixed-Point Theorem and its applications, such as Picard's Existence and Uniqueness Theorem, through the basics of linear operators, two of the three fundamental principles (the Uniform Boundedness Principle and the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems), to the elements of the spectral theory, including Gelfand's Spectral Radius Theorem and the Spectral Theorem for Compact Self-Adjoint Operators, and its applications, such as the celebrated Lyapunov Stability Theorem. Conceived as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. There are problems at the end of each chapter, starting with Chapter 2 and totaling at 150. Many important statements are given as problems and frequently referred to in the main body. There are also 432 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in certain details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problems and exercises are supplied with "existential'' hints. The book is generous on Examples and contains numerous Remarks accompanying definitions, examples, and statements to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. With carefully chosen material, proper attention given to applications, and plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester Master's level graduate course in operator theory with emphasis on spectral theory for students majoring in mathematics, physics, computer science, and engineering. Contents Preface Preliminaries Metric Spaces Vector Spaces, Normed Vector Spaces, and Banach Spaces Linear Operators Elements of Spectral Theory in a Banach Space Setting Elements of Spectral Theory in a Hilbert Space Setting Appendix: The Axiom of Choice and Equivalents Bibliography Index
Norm Estimations For Operator Valued Functions And Their Applications
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Author : Michael Gil
language : en
Publisher: CRC Press
Release Date : 2021-06-30
Norm Estimations For Operator Valued Functions And Their Applications written by Michael Gil and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-30 with Mathematics categories.
Intended for specialists in functional analysis and stability theory, this work presents a systematic exposition of estimations for norms of operator-valued functions, and applies the estimates to spectrum perturbations of linear operators and stability theory. The author demonstrates his own approach to spectrum perturbations.
Perturbation Theory For Linear Operators
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Author : Aref Jeribi
language : en
Publisher: Springer Nature
Release Date : 2021-07-28
Perturbation Theory For Linear Operators written by Aref Jeribi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-28 with Mathematics categories.
This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.
Lie Groups Lie Algebras And Representations
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Author : Brian C. Hall
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-08-07
Lie Groups Lie Algebras And Representations written by Brian C. Hall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-07 with Education categories.
This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.