Hilbert Spaces
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Introduction To Hilbert Spaces With Applications
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Author : Lokenath Debnath
language : en
Publisher: Academic Press
Release Date : 2005-09-29
Introduction To Hilbert Spaces With Applications written by Lokenath Debnath and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-29 with Mathematics categories.
"Continuing on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory complemented by a variety of applications. Students and researchers will benefit from the enhanced presentation of results and proofs and new and revised examples. A completely new section on Sobolev spaces has been added, and the treatment of finite dimensional normed spaces has been expanded. The chapter on wavelets has been updated."--BOOK JACKET.
Introduction To Hilbert Space
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Author : Sterling K. Berberian
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Introduction To Hilbert Space written by Sterling K. Berberian 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 1999 with Mathematics categories.
From the Preface: ``This textbook has evolved from a set of lecture notes ... In both the course and the book, I have in mind first- or second-year graduate students in Mathematics and related fields such as Physics ... It is necessary for the reader to have a foundation in advanced calculus which includes familiarity with: least upper bound (LUB) and greatest lower bound (GLB), the concept of function, $\epsilon$'s and their companion $\delta$'s, and basic properties of sequences of real and complex numbers (convergence, Cauchy's criterion, the Weierstrass-Bolzano theorem). It is not presupposed that the reader is acquainted with vector spaces ... , matrices ... , or determinants ... There are over four hundred exercises, most of them easy ... It is my hope that this book, aside from being an exposition of certain basic material on Hilbert space, may also serve as an introduction to other areas of functional analysis.''
A Primer On Hilbert Space Theory
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Author : Carlo Alabiso
language : en
Publisher: Springer Nature
Release Date : 2021-03-03
A Primer On Hilbert Space Theory written by Carlo Alabiso and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-03 with Science categories.
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.
Hilbert Spaces Wavelets Generalised Functions And Modern Quantum Mechanics
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Author : W.-H. Steeb
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Hilbert Spaces Wavelets Generalised Functions And Modern Quantum Mechanics written by W.-H. Steeb 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 2013-03-07 with Science categories.
This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. Audience: The book is suitable for graduate students in physics and mathematics.
An Introduction To Hilbert Space
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Author : N. Young
language : en
Publisher: Cambridge University Press
Release Date : 1988-07-21
An Introduction To Hilbert Space written by N. Young 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 1988-07-21 with Mathematics categories.
The notion of a Hilbert space is a central idea in functional analysis and this text demonstrates its applications in numerous branches of pure and applied mathematics.
Functional Analysis
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Author : Joseph Muscat
language : en
Publisher: Springer
Release Date : 2014-07-23
Functional Analysis written by Joseph Muscat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Mathematics categories.
This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.
Hilbert Spaces
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Author :
language : en
Publisher: Elsevier
Release Date : 2001-07-11
Hilbert Spaces written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-11 with Mathematics categories.
This book has evolved from the lecture course on Functional Analysis I had given several times at the ETH. The text has a strict logical order, in the style of “Definition – Theorem – Proof - Example - Exercises . The proofs are rather thorough and there many examples. The first part of the book(the first three chapters, resp. the first two volumes) is devoted to the theory of Banach spaces in the most general sense of the term. The purpose of the first chapter (resp. first volume) is to introduce those results on Banach spaces which are used later or which are closely connected with the book. It therefore only contains a small part of the theory, and several results are stated (and proved) in a diluted form. The second chapter (which together with Chapter 3 makes the second volume) deals with Banach algebras (and involutive Banach algebras), which constitute the main topic of the first part of the book. The third chapter deals with compact operators on Banach spaces and linear (ordinary and partial) differential equations - applications of the, theory of Banach algebras.
Elements Of Hilbert Spaces And Operator Theory
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Author : Harkrishan Lal Vasudeva
language : en
Publisher: Springer
Release Date : 2017-03-27
Elements Of Hilbert Spaces And Operator Theory written by Harkrishan Lal Vasudeva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-27 with Mathematics categories.
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.
Hilbert Spaces And Operator Theory
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Author : W. Mlak
language : en
Publisher: Springer
Release Date : 1991-11-30
Hilbert Spaces And Operator Theory written by W. Mlak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-30 with Mathematics categories.
Emphasizing a clear exposition for readers familiar with elementary measure theory and the fundamentals of set theory and general topology, presents the basic notions and methods of the theory of Hilbert spaces, a part of functional analysis being increasingly applied in mathematics and theoretical
Spectral Theory Of Operators On Hilbert Spaces
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Author : Carlos S. Kubrusly
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-01
Spectral Theory Of Operators On Hilbert Spaces written by Carlos S. Kubrusly 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 2012-06-01 with Mathematics categories.
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.