A Short Introduction To Perturbation Theory For Linear Operators

Author : Tosio Kato
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461257004

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A Short Introduction to Perturbation Theory for Linear Operators by Tosio Kato Pdf

This book is a slightly expanded reproduction of the first two chapters (plus Introduction) of my book Perturbation Theory tor Linear Operators, Grundlehren der mathematischen Wissenschaften 132, Springer 1980. Ever since, or even before, the publication of the latter, there have been suggestions about separating the first two chapters into a single volume. I have now agreed to follow the suggestions, hoping that it will make the book available to a wider audience. Those two chapters were intended from the outset to be a comprehen sive presentation of those parts of perturbation theory that can be treated without the topological complications of infinite-dimensional spaces. In fact, many essential and. even advanced results in the theory have non trivial contents in finite-dimensional spaces, although one should not forget that some parts of the theory, such as those pertaining to scatter ing. are peculiar to infinite dimensions. I hope that this book may also be used as an introduction to linear algebra. I believe that the analytic approach based on a systematic use of complex functions, by way of the resolvent theory, must have a strong appeal to students of analysis or applied mathematics, who are usually familiar with such analytic tools.

Author : Tosio Kato
Publisher : Springer Science & Business Media
Page : 610 pages
File Size : 42,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662126783

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Perturbation theory for linear operators by Tosio Kato Pdf

Author : Tosio Kato
Publisher : Springer
Page : 619 pages
File Size : 43,9 Mb
Release : 1995-01-01
Category : Linear operators.
ISBN : 038758661X

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Perturbation Theory for Linear Operators by Tosio Kato Pdf

Author : Anonim
Publisher : Unknown
Page : 619 pages
File Size : 46,7 Mb
Release : 1976
Category : Linear operators
ISBN : OCLC:911752383

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Perturbation Theory for Linear Operators by Anonim Pdf

Author : Aref Jeribi
Publisher : Springer Nature
Page : 509 pages
File Size : 53,5 Mb
Release : 2021-07-28
Category : Mathematics
ISBN : 9789811625282

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Perturbation Theory for Linear Operators by Aref Jeribi Pdf

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.

Author : J.T. Oden,J.N. Reddy
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642688119

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Variational Methods in Theoretical Mechanics by J.T. Oden,J.N. Reddy Pdf

This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. We also gratefully acknowedge that much of our own research work on va ri at i ona 1 theory was supported by the U. S. Ai r Force Offi ce of Scientific Research. We are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and painstaking job of typing the manuscript. This revised edition contains only minor revisions of the first. Some misprints and errors have been corrected, and some sections were deleted, which were felt to be out of date.

Author : Diederich Hinrichsen,Anthony J. Pritchard
Publisher : Springer Science & Business Media
Page : 818 pages
File Size : 49,7 Mb
Release : 2005-10-28
Category : Mathematics
ISBN : 9783540264101

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Mathematical Systems Theory I by Diederich Hinrichsen,Anthony J. Pritchard Pdf

This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. It is devoted to the analysis of dynamical systems and combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions.

Author : Yifeng Xue
Publisher : World Scientific
Page : 304 pages
File Size : 51,6 Mb
Release : 2012-03-16
Category : Mathematics
ISBN : 9789814452809

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Stable Perturbations of Operators and Related Topics by Yifeng Xue Pdf

This book provides a broad introduction to the generalized inverses, Moore–Penrose inverses, Drazin inverses and T–S outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operator algebras, global analysis and approximation theory and so on. Stable Perturbations of Operators and Related Topics is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students. It is also suitable for researchers as a reference. The proofs of statements and explanations in the book are detailed enough that interested readers can study it by themselves. Contents:Basics in Functional AnalysisStable Perturbation of Densely-Defined Closed OperatorsMoore–Penrose Inverse and Its Stable PerturbationDrazin Inverses, T–S Generalized Inverses and Their PerturbationsMiscellaneous ApplicationsSome Related Topics Readership: Graduate students and researchers in analysis and differential equations, numerical analysis and computational mathematics, algebra. Keywords:Generalized Inverse;Moore–Penrose Inverse;Drazin Inverse;Stable PerturbationKey Features:The stable perturbation theory of generalized inverses, Drazin inverses and index of a Fredholm element relative to a homomorphismare are of unique interest in this book The stable perturbation theory of generalized inverses is a very useful tool in studying the perturbations of Moore–Penrose inverses and Drazin inverses. It also has important applications in Operator Theory, Operator Algebras and Global Analysis. All these are described completely in the bookThe expression and index of the perturbed Drazin inverse of a Drazin invertible operator or element under stable perturbation are very useful in computing the Drazin inverses of certain operators and elements and estimating the error-bounds of the perturbations. It can not be found in current books concerning the Drazin inversesThe Toeplitz operator and its index is a very interesting topic in the Mathematical World. In this book, we define a generalized Toeplitz element in a Banach algebra and establish its index formula. Using it, we can deduce the indices formulae of some classical Toeplitz operators. This theory is new and very usefulReviews: "This book may be of some interest to specialists." Zentralblatt MATH

Author : H. Baumgärtel
Publisher : Walter de Gruyter GmbH & Co KG
Page : 428 pages
File Size : 51,8 Mb
Release : 1984-12-31
Category : Mathematics
ISBN : 9783112721810

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Analytic Perturbation Theory for Matrices and Operators by H. Baumgärtel Pdf

No detailed description available for "Analytic Perturbation Theory for Matrices and Operators".

Author : Baumgärtel
Publisher : Springer
Page : 446 pages
File Size : 49,8 Mb
Release : 1985
Category : Juvenile Nonfiction
ISBN : UCAL:B4128227

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Analytic Perturbation Theory for Matrices and Operators by Baumgärtel Pdf

Author : Ronald E. Mickens
Publisher : World Scientific
Page : 261 pages
File Size : 43,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814291651

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Truly Nonlinear Oscillations by Ronald E. Mickens Pdf

This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of "truly nonlinear" (TNL) oscillator equations. The volume gives a general overview of the author's work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a direct comparison to be made among the various methods. The book is self-contained and therefore suitable for both classroom use and self-study by students and professionals who desire to learn, understand, and apply this technique to the field of nonlinear oscillations.

Author : Akiva M. Yaglom
Publisher : Springer Science & Business Media
Page : 611 pages
File Size : 45,7 Mb
Release : 2012-12-18
Category : Technology & Engineering
ISBN : 9789400742376

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Hydrodynamic Instability and Transition to Turbulence by Akiva M. Yaglom Pdf

This book is a complete revision of the part of Monin & Yaglom's famous two-volume work "Statistical Fluid Mechanics: Mechanics of Turbulence" that deals with the theory of laminar-flow instability and transition to turbulence. It includes the considerable advances in the subject that have been made in the last 15 years or so. It is intended as a textbook for advanced graduate courses and as a reference for research students and professional research workers. The first two Chapters are an introduction to the mathematics, and the experimental results, for the instability of laminar (or inviscid) flows to infinitesimal (in practice "small") disturbances. The third Chapter develops this linear theory in more detail and describes its application to particular problems. Chapters 4 and 5 deal with instability to finite-amplitude disturbances: much of the material has previously been available only in research papers.

Author : Helmut Wielandt
Publisher : Walter de Gruyter
Page : 660 pages
File Size : 44,8 Mb
Release : 1996
Category : Mathematics
ISBN : 311012453X

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Mathematical works by Helmut Wielandt Pdf

Author : Shmuel Friedland
Publisher : World Scientific
Page : 595 pages
File Size : 41,7 Mb
Release : 2015-10-29
Category : Mathematics
ISBN : 9789814667975

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Matrices by Shmuel Friedland Pdf

"This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry and numerical analysis. It consists of seven chapters that are loosely connected and interdependent. The choice of the topics is very personal and reflects the subjects that the author was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume is also devoted to various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of non-negative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operations research, physics and statistics."--

Author : Oscar Gonzalez
Publisher : American Mathematical Society
Page : 228 pages
File Size : 55,8 Mb
Release : 2022-12-05
Category : Mathematics
ISBN : 9781470469917

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Topics in Applied Mathematics and Modeling by Oscar Gonzalez Pdf

The analysis and interpretation of mathematical models is an essential part of the modern scientific process. Topics in Applied Mathematics and Modeling is designed for a one-semester course in this area aimed at a wide undergraduate audience in the mathematical sciences. The prerequisite for access is exposure to the central ideas of linear algebra and ordinary differential equations. The subjects explored in the book are dimensional analysis and scaling, dynamical systems, perturbation methods, and calculus of variations. These are immense subjects of wide applicability and a fertile ground for critical thinking and quantitative reasoning, in which every student of mathematics should have some experience. Students who use this book will enhance their understanding of mathematics, acquire tools to explore meaningful scientific problems, and increase their preparedness for future research and advanced studies. The highlights of the book are case studies and mini-projects, which illustrate the mathematics in action. The book also contains a wealth of examples, figures, and regular exercises to support teaching and learning. The book includes opportunities for computer-aided explorations, and each chapter contains a bibliography with references covering further details of the material.