Linear Operators And Linear Systems

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Linear Operators And Linear Systems

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Author : Jonathan R. Partington
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-15

Linear Operators And Linear Systems written by Jonathan R. Partington and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-15 with Mathematics categories.

Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering.

Linear Algebra And Linear Operators In Engineering

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Author : H. Ted Davis
language : en
Publisher: Elsevier
Release Date : 2000-07-12

Linear Algebra And Linear Operators In Engineering written by H. Ted Davis and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-12 with Mathematics categories.

Designed for advanced engineering, physical science, and applied mathematics students, this innovative textbook is an introduction to both the theory and practical application of linear algebra and functional analysis. The book is self-contained, beginning with elementary principles, basic concepts, and definitions. The important theorems of the subject are covered and effective application tools are developed, working up to a thorough treatment of eigenanalysis and the spectral resolution theorem. Building on a fundamental understanding of finite vector spaces, infinite dimensional Hilbert spaces are introduced from analogy. Wherever possible, theorems and definitions from matrix theory are called upon to drive the analogy home. The result is a clear and intuitive segue to functional analysis, culminating in a practical introduction to the functional theory of integral and differential operators. Numerous examples, problems, and illustrations highlight applications from all over engineering and the physical sciences. Also included are several numerical applications, complete with Mathematica solutions and code, giving the student a "hands-on" introduction to numerical analysis. Linear Algebra and Linear Operators in Engineering is ideally suited as the main text of an introductory graduate course, and is a fine instrument for self-study or as a general reference for those applying mathematics. - Contains numerous Mathematica examples complete with full code and solutions - Provides complete numerical algorithms for solving linear and nonlinear problems - Spans elementary notions to the functional theory of linear integral and differential equations - Includes over 130 examples, illustrations, and exercises and over 220 problems ranging from basic concepts to challenging applications - Presents real-life applications from chemical, mechanical, and electrical engineering and the physical sciences

Linear Operator Equations Approximation And Regularization

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Author : M Thamban Nair
language : en
Publisher: World Scientific
Release Date : 2009-05-05

Linear Operator Equations Approximation And Regularization written by M Thamban Nair and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-05 with Mathematics categories.

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.

Traces And Determinants Of Linear Operators

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Author : Israel Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Traces And Determinants Of Linear Operators written by Israel Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The authors initially planned to write an article describing the origins and devel opments of the theory of Fredholm operators and to present their recollections of this topic. We started to read again classical papers and we were sidetracked by the literature concerned with the theory and applications of traces and determi nants of infinite matrices and integral operators. We were especially impressed by the papers of Poincare, von Koch, Fredholm, Hilbert and Carleman, as well as F. Riesz's book on infinite systems of linear equations. Consequently our plans were changed and we decided to write a paper on the history of determinants of infi nite matrices and operators. During the preparation of our paper we realized that many mathematical questions had to be answered in order to gain a more com plete understanding of the subject. So, we changed our plans again and decided to present the subject in a more advanced form which would satisfy our new require ments. This whole process took between four and five years of challenging, but enjoyable work. This entailed the study of the appropriate relatively recent results of Grothendieck, Ruston, Pietsch, Hermann Konig and others. After the papers [GGK1] and [GGK2] were published, we saw that the written material could serve as the basis of a book.

Dynamics Of Linear Operators

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Author : Frédéric Bayart
language : en
Publisher: Cambridge University Press
Release Date : 2009-06-04

Dynamics Of Linear Operators written by Frédéric Bayart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-04 with Mathematics categories.

The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.

Linear Operators In Hilbert Spaces

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Author : Joachim Weidmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Linear Operators In Hilbert Spaces written by Joachim Weidmann 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 2012-12-06 with Mathematics categories.

This English edition is almost identical to the German original Lineare Operatoren in Hilbertriiumen, published by B. G. Teubner, Stuttgart in 1976. A few proofs have been simplified, some additional exercises have been included, and a small number of new results has been added (e.g., Theorem 11.11 and Theorem 11.23). In addition a great number of minor errors has been corrected. Frankfurt, January 1980 J. Weidmann vii Preface to the German edition The purpose of this book is to give an introduction to the theory of linear operators on Hilbert spaces and then to proceed to the interesting applica tions of differential operators to mathematical physics. Besides the usual introductory courses common to both mathematicians and physicists, only a fundamental knowledge of complex analysis and of ordinary differential equations is assumed. The most important results of Lebesgue integration theory, to the extent that they are used in this book, are compiled with complete proofs in Appendix A. I hope therefore that students from the fourth semester on will be able to read this book without major difficulty. However, it might also be of some interest and use to the teaching and research mathematician or physicist, since among other things it makes easily accessible several new results of the spectral theory of differential 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.

Semigroups Of Linear Operators And Applications

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Author : Jerome A. Goldstein
language : en
Publisher: Courier Dover Publications
Release Date : 2017-05-17

Semigroups Of Linear Operators And Applications written by Jerome A. Goldstein and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-17 with Mathematics categories.

Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.

Spectral Approximation Of Linear Operators

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Author : Françoise Chaitin-Chatelin
language : en
Publisher:
Release Date : 1983

Spectral Approximation Of Linear Operators written by Françoise Chaitin-Chatelin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

The goal of this book is to be comprehensive, running the gamut from practical numerical results to a unifying framework of functional analysis, while simultaneously preserving the energy and excitement of presenting fresh research results. Its contents cover recent results, which either are scattered through the literature or appear here for the first time, as well as providing a nontraditional presentation of standard material.

Linear Operator Theory In Engineering And Science

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Author : Arch W. Naylor
language : en
Publisher: Springer Science & Business Media
Release Date : 1982

Linear Operator Theory In Engineering And Science written by Arch W. Naylor 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 1982 with Mathematics categories.

This book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.