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Author: Piotr Sołtan
Publisher: Springer
ISBN: 3319920618
Category : Mathematics
Languages : en
Pages : 200
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Book Description
The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators. The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.
Author: Piotr Sołtan
Publisher: Springer
ISBN: 3319920618
Category : Mathematics
Languages : en
Pages : 200
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Book Description
The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators. The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.
Author: Carlo Alabiso
Publisher: Springer Nature
ISBN: 3030674177
Category : Science
Languages : en
Pages : 343
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Book Description
This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
Author: V. S. Sunder
Publisher: Springer
ISBN: 9811018162
Category : Mathematics
Languages : en
Pages : 100
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Book Description
The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators.
Author: Carlos S. Kubrusly
Publisher: Springer Science & Business Media
ISBN: 1461220645
Category : Mathematics
Languages : en
Pages : 162
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Book Description
This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that range from the straightforward to the state-of-the-art. Complete solutions to all problems are provided. The text covers the basics of bounded linear operators on a Hilbert space and gradually progresses to more advanced topics in spectral theory and quasireducible operators. Written in a motivating and rigorous style, the work has few prerequisites beyond elementary functional analysis, and will appeal to graduate students and researchers in mathematics, physics, engineering, and related disciplines.
Author: Ruben A. Martinez-Avendano
Publisher: Springer Science & Business Media
ISBN: 0387485783
Category : Mathematics
Languages : en
Pages : 230
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Book Description
This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
Author: Jirí Blank
Publisher: Springer Science & Business Media
ISBN: 9781563961427
Category : Science
Languages : en
Pages : 626
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Book Description
Market: Mathematicians, researchers, teachers, and graduate students specializing in quantum physics, mathematical physics, and applied mathematics. "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone....The translation is remarkably good." John R. Taylor, University of Colorado Based on lectures delivered over the past two decades, this book explains in detail the theory of linear Hilbert-space operators and its uses in quantum physics. The central mathematical tool of this book is the spectral theory of self-adjoint operators, which together with functional analysis and an introduction to the theory of operator sets and algebras, is used in a systematic analysis of the operator aspect of quantum theory. In addition, the theory of Hilbert-space operators is discussed in conjunction with various applications such as Schrodinger operators and scattering theory.
Author: Kurt O. Friedrichs
Publisher: Springer Science & Business Media
ISBN: 1461263964
Category : Mathematics
Languages : en
Pages : 253
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Book Description
The present lectures intend to provide an introduction to the spectral analysis of self-adjoint operators within the framework of Hilbert space theory. The guiding notion in this approach is that of spectral representation. At the same time the notion of function of an operator is emphasized. The formal aspects of these concepts are explained in the first two chapters. Only then is the notion of Hilbert space introduced. The following three chapters concern bounded, completely continuous, and non-bounded operators. Next, simple differential operators are treated as operators in Hilbert space, and the final chapter deals with the perturbation of discrete and continuous spectra. The preparation of the original version of these lecture notes was greatly helped by the assistance of P. Rejto. Various valuable suggestions made by him and by R. Lewis have been incorporated. The present version of the notes contains extensive modifica tions, in particular in the chapters on bounded and unbounded operators. February, 1973 K.O.F. PREFACE TO THE SECOND PRINTING The second printing (1980) is a basically unchanged reprint in which a number of minor errors were corrected. The author wishes to thank Klaus Schmidt (Lausanne) and John Sylvester (New York) for their lists of errors. v TABLE OF CONTENTS I. Spectral Representation 1 1. Three typical problems 1 12 2. Linear space and functional representation.
Author: Carlos S. Kubrusly
Publisher: Springer Science & Business Media
ISBN: 0817683283
Category : Mathematics
Languages : en
Pages : 203
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Book Description
This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Spaces is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to apply spectral theory to their field.
Author: Sheldon Axler
Publisher: Springer Science & Business Media
ISBN: 3034603479
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Paul Richard Halmos, who lived a life of unbounded devotion to mathematics and to the mathematical community, died at the age of 90 on October 2, 2006. This volume is a memorial to Paul by operator theorists he inspired. Paul’sinitial research,beginning with his 1938Ph.D. thesis at the University of Illinois under Joseph Doob, was in probability, ergodic theory, and measure theory. A shift occurred in the 1950s when Paul’s interest in foundations led him to invent a subject he termed algebraic logic, resulting in a succession of papers on that subject appearing between 1954 and 1961, and the book Algebraic Logic, published in 1962. Paul’s ?rst two papers in pure operator theory appeared in 1950. After 1960 Paul’s research focused on Hilbert space operators, a subject he viewed as enc- passing ?nite-dimensional linear algebra. Beyond his research, Paul contributed to mathematics and to its community in manifold ways: as a renowned expositor, as an innovative teacher, as a tireless editor, and through unstinting service to the American Mathematical Society and to the Mathematical Association of America. Much of Paul’s in?uence ?owed at a personal level. Paul had a genuine, uncalculating interest in people; he developed an enormous number of friendships over the years, both with mathematicians and with nonmathematicians. Many of his mathematical friends, including the editors ofthisvolume,whileabsorbingabundantquantitiesofmathematicsatPaul’sknee, learned from his advice and his example what it means to be a mathematician.
Author: Sterling K. Berberian
Publisher: Chelsea Publishing Company, Incorporated
ISBN:
Category : Mathematics
Languages : en
Pages : 232
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Book Description
