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Introduction To Linear Operator Theory
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Book Synopsis Introduction to Linear Operator Theory by : Vasile I. Istratescu
Download or read book Introduction to Linear Operator Theory written by Vasile I. Istratescu and published by CRC Press. This book was released on 2020-08-14 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the subject and is devoted to standard material on linear functional analysis, and presents some ergodic theorems for classes of operators containing the quasi-compact operators. It discusses various classes of operators connected with the numerical range.
Book Synopsis Linear Operator Theory in Engineering and Science by : Arch W. Naylor
Download or read book Linear Operator Theory in Engineering and Science written by Arch W. Naylor and published by Springer Science & Business Media. This book was released on 1982 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Linear Operator Theory by : Vasile I. Istratescu
Download or read book Introduction to Linear Operator Theory written by Vasile I. Istratescu and published by CRC Press. This book was released on 2020-08-13 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the subject and is devoted to standard material on linear functional analysis, and presents some ergodic theorems for classes of operators containing the quasi-compact operators. It discusses various classes of operators connected with the numerical range.
Book Synopsis Theory of Linear Operations by : S. Banach
Download or read book Theory of Linear Operations written by S. Banach and published by Elsevier. This book was released on 1987-03-01 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra. The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series. A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.
Book Synopsis Introduction to Operator Theory I by : A. Brown
Download or read book Introduction to Operator Theory I written by A. Brown and published by Springer. This book was released on 1977-12-19 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was written expressly to serve as a textbook for a one- or two-semester introductory graduate course in functional analysis. Its (soon to be published) companion volume, Operators on Hilbert Space, is in tended to be used as a textbook for a subsequent course in operator theory. In writing these books we have naturally been concerned with the level of preparation of the potential reader, and, roughly speaking, we suppose him to be familiar with the approximate equivalent of a one-semester course in each of the following areas: linear algebra, general topology, complex analysis, and measure theory. Experience has taught us, however, that such a sequence of courses inevitably fails to treat certain topics that are important in the study of functional analysis and operator theory. For example, tensor products are frequently not discussed in a first course in linear algebra. Likewise for the topics of convergence of nets and the Baire category theorem in a course in topology, and the connections between measure and topology in a course in measure theory. For this reason we have chosen to devote the first ten chapters of this volume (entitled Part I) to topics of a preliminary nature. In other words, Part I summarizes in considerable detail what a student should (and eventually must) know in order to study functional analysis and operator theory successfully.
Book Synopsis Perturbation theory for linear operators by : Tosio Kato
Download or read book Perturbation theory for linear operators written by Tosio Kato and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by : Tailen Hsing
Download or read book Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators written by Tailen Hsing and published by John Wiley & Sons. This book was released on 2015-05-06 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.
Book Synopsis Basic Operator Theory by : Israel Gohberg
Download or read book Basic Operator Theory written by Israel Gohberg and published by Birkhäuser. This book was released on 2013-12-01 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spectral Theory of Linear Operators by : Vladimir Müller
Download or read book Spectral Theory of Linear Operators written by Vladimir Müller and published by Springer Science & Business Media. This book was released on 2007-12-24 with total page 439 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.
Book Synopsis An Introduction to Models and Decompositions in Operator Theory by : Carlos S. Kubrusly
Download or read book An Introduction to Models and Decompositions in Operator Theory written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a Hilbert-space operator we mean a bounded linear transformation be tween separable complex Hilbert spaces. Decompositions and models for Hilbert-space operators have been very active research topics in operator theory over the past three decades. The main motivation behind them is the in variant subspace problem: does every Hilbert-space operator have a nontrivial invariant subspace? This is perhaps the most celebrated open question in op erator theory. Its relevance is easy to explain: normal operators have invariant subspaces (witness: the Spectral Theorem), as well as operators on finite dimensional Hilbert spaces (witness: canonical Jordan form). If one agrees that each of these (i. e. the Spectral Theorem and canonical Jordan form) is important enough an achievement to dismiss any further justification, then the search for nontrivial invariant subspaces is a natural one; and a recalcitrant one at that. Subnormal operators have nontrivial invariant subspaces (extending the normal branch), as well as compact operators (extending the finite-dimensional branch), but the question remains unanswered even for equally simple (i. e. simple to define) particular classes of Hilbert-space operators (examples: hyponormal and quasinilpotent operators). Yet the invariant subspace quest has certainly not been a failure at all, even though far from being settled. The search for nontrivial invariant subspaces has undoubtly yielded a lot of nice results in operator theory, among them, those concerning decompositions and models for Hilbert-space operators. This book contains nine chapters.
Book Synopsis Introduction to Operator Theory in Riesz Spaces by : Adriaan C. Zaanen
Download or read book Introduction to Operator Theory in Riesz Spaces written by Adriaan C. Zaanen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the beginning of the thirties a considerable number of books on func tional analysis has been published. Among the first ones were those by M. H. Stone on Hilbert spaces and by S. Banach on linear operators, both from 1932. The amount of material in the field of functional analysis (in cluding operator theory) has grown to such an extent that it has become impossible now to include all of it in one book. This holds even more for text books. Therefore, authors of textbooks usually restrict themselves to normed spaces (or even to Hilbert space exclusively) and linear operators in these spaces. In more advanced texts Banach algebras and (or) topological vector spaces are sometimes included. It is only rarely, however, that the notion of order (partial order) is explicitly mentioned (even in more advanced exposi tions), although order structures occur in a natural manner in many examples (spaces of real continuous functions or spaces of measurable function~). This situation is somewhat surprising since there exist important and illuminating results for partially ordered vector spaces, in . particular for the case that the space is lattice ordered. Lattice ordered vector spaces are called vector lattices or Riesz spaces. The first results go back to F. Riesz (1929 and 1936), L. Kan torovitch (1935) and H. Freudenthal (1936).
Book Synopsis Elements of Hilbert Spaces and Operator Theory by : Harkrishan Lal Vasudeva
Download or read book Elements of Hilbert Spaces and Operator Theory written by Harkrishan Lal Vasudeva and published by Springer. This book was released on 2017-03-27 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators. In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.
Book Synopsis Elements of Functional Analysis by : Arlen Brown
Download or read book Elements of Functional Analysis written by Arlen Brown and published by . This book was released on 1977 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operator Theory for Electromagnetics by : George W. Hanson
Download or read book Operator Theory for Electromagnetics written by George W. Hanson and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses electromagnetics from the view of operator theory, in a manner more commonly seen in textbooks of quantum mechanics. It includes a self-contained introduction to operator theory, presenting definitions and theorems, plus proofs of the theorems when these are simple or enlightening.
Book Synopsis Basic Classes of Linear Operators by : Israel Gohberg
Download or read book Basic Classes of Linear Operators written by Israel Gohberg and published by Springer Science & Business Media. This book was released on 2003-10-24 with total page 448 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.
Book Synopsis Introduction to the Theory of Linear Nonselfadjoint Operators by : Israel Gohberg
Download or read book Introduction to the Theory of Linear Nonselfadjoint Operators written by Israel Gohberg and published by American Mathematical Soc.. This book was released on 1978 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Functional Analysis by : Hans Wilhelm Alt
Download or read book Linear Functional Analysis written by Hans Wilhelm Alt and published by Springer. This book was released on 2016-07-06 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.
