Introduction To Hilbert Space And The Theory Of Spectral Multiplicity
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Introduction To Hilbert Space And The Theory Of Spectral Multiplicity
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Author : Paul R. Halmos
language : en
Publisher: Courier Dover Publications
Release Date : 2017-12-13
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity written by Paul R. Halmos 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 2017-12-13 with Mathematics categories.
This concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. Author Paul R. Halmos notes in the Preface that his motivation in writing this text was to make available to a wider audience the results of the third chapter, the so-called multiplicity theory. The theory as he presents it deals with arbitrary spectral measures, including the multiplicity theory of normal operators on a not necessarily separable Hilbert space. His explication covers, as another useful special case, the multiplicity theory of unitary representations of locally compact abelian groups. Suitable for advanced undergraduates and graduate students in mathematics, this volume's sole prerequisite is a background in measure theory. The distinguished mathematician E. R. Lorch praised the book in the Bulletin of the American Mathematical Society as "an exposition which is always fresh, proofs which are sophisticated, and a choice of subject matter which is certainly timely."
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity
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Author : Paul R. Halmos
language : en
Publisher:
Release Date : 2013-09
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity written by Paul R. Halmos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09 with Mathematics categories.
2013 Reprint of 1951 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. The subject matter of the book is funneled into three chapters: [1] The geometry of Hubert space; [2] the structure of self-adjoint and normal operators; [3] and multiplicity theory for a normal operator. For the last, an expert knowledge of measure theory is indispensable. Indeed, multiplicity theory is a magnificent measure-theoretic tour de force. The subject matter of the first two chapters might be said to constitute an introduction to Hilbert space, and for these, an a priori knowledge of classic measure theory is not essential. Paul Richard Halmos (1916-2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity
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Author : Paul Richard Halmos
language : en
Publisher:
Release Date : 1960
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity written by Paul Richard Halmos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Hilbert space categories.
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity
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Author : Paul R (Paul Richard) 1916- Halmos
language : en
Publisher: Hassell Street Press
Release Date : 2021-09-10
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity written by Paul R (Paul Richard) 1916- Halmos and has been published by Hassell Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-10 with categories.
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity Halmos
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Author : Paul Richard Halmos
language : en
Publisher:
Release Date :
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity Halmos written by Paul Richard Halmos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity
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Author : James Bryant Conant
language : en
Publisher:
Release Date : 1957
Introduction To Hilbert Space And The Theory Of Spectral Multiplicity written by James Bryant Conant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with categories.
A Hilbert Space Problem Book
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Author : P.R. Halmos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Hilbert Space Problem Book written by P.R. Halmos 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.
From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
Introduction To Hilbert Space
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Author :
language : en
Publisher:
Release Date : 1951
Introduction To Hilbert Space written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1951 with Hilbert space categories.
Spectral Theory Of Ordinary Differential Operators
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Author : Joachim Weidmann
language : en
Publisher: Springer
Release Date : 2006-11-15
Spectral Theory Of Ordinary Differential Operators written by Joachim Weidmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.
Lectures On Ergodic Theory
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Author : Paul Richard Halmos
language : en
Publisher: American Mathematical Soc.
Release Date : 1956
Lectures On Ergodic Theory written by Paul Richard Halmos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with Mathematics categories.
This classic book is based on lectures given by the author at the University of Chicago in 1956. The topics covered include, in particular, recurrence, the ergodic theorems, and a general discussion of ergodicity and mixing properties. There is also a general discussion of the relation between conjugacy and equivalence. With minimal prerequisites of some analysis and measure theory, this work can be used for a one-semester course in ergodic theory or for self-study.