Introduction To Hilbert Space

Author : N. Young
Publisher : Cambridge University Press
Page : 254 pages
File Size : 49,6 Mb
Release : 1988-07-21
Category : Mathematics
ISBN : 9781107717169

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An Introduction to Hilbert Space by N. Young Pdf

This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.

Author : David W. Cohen
Publisher : Springer Science & Business Media
Page : 159 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461388418

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An Introduction to Hilbert Space and Quantum Logic by David W. Cohen Pdf

Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.

Author : Sterling K. Berberian
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 50,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821819128

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Introduction to Hilbert Space by Sterling K. Berberian Pdf

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.''

Author : Gerald B. Folland
Publisher : John Wiley & Sons
Page : 368 pages
File Size : 41,9 Mb
Release : 2013-06-11
Category : Mathematics
ISBN : 9781118626399

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Real Analysis by Gerald B. Folland Pdf

An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.

Author : Lokenath Debnath,Piotr Mikusinski
Publisher : Elsevier
Page : 600 pages
File Size : 49,5 Mb
Release : 2005-09-29
Category : Mathematics
ISBN : 9780080455921

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Introduction to Hilbert Spaces with Applications by Lokenath Debnath,Piotr Mikusinski Pdf

Building 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 and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory. Updated chapter on wavelets Improved presentation on results and proof Revised examples and updated applications Completely updated list of references

Author : Gilbert Helmberg
Publisher : Elsevier
Page : 362 pages
File Size : 47,8 Mb
Release : 2014-11-28
Category : Science
ISBN : 9781483164175

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Introduction to Spectral Theory in Hilbert Space by Gilbert Helmberg Pdf

North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.

Author : N. Young
Publisher : Cambridge University Press
Page : 254 pages
File Size : 46,5 Mb
Release : 1988-07-21
Category : Mathematics
ISBN : 0521337178

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An Introduction to Hilbert Space by N. Young Pdf

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.

Author : P.R. Halmos
Publisher : Springer Science & Business Media
Page : 385 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493306

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A Hilbert Space Problem Book by P.R. Halmos Pdf

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."

Author : Samuel S. Holland
Publisher : Courier Corporation
Page : 578 pages
File Size : 41,5 Mb
Release : 2012-05-04
Category : Mathematics
ISBN : 9780486139296

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Applied Analysis by the Hilbert Space Method by Samuel S. Holland Pdf

Numerous worked examples and exercises highlight this unified treatment. Simple explanations of difficult subjects make it accessible to undergraduates as well as an ideal self-study guide. 1990 edition.

Author : Ruben A. Martinez-Avendano,Peter Rosenthal
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 50,8 Mb
Release : 2007-03-12
Category : Mathematics
ISBN : 9780387485782

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An Introduction to Operators on the Hardy-Hilbert Space by Ruben A. Martinez-Avendano,Peter Rosenthal Pdf

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 : Paul R. Halmos
Publisher : Courier Dover Publications
Page : 129 pages
File Size : 54,5 Mb
Release : 2017-11-15
Category : Mathematics
ISBN : 9780486826837

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Introduction to Hilbert Space and the Theory of Spectral Multiplicity by Paul R. Halmos Pdf

Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.

Author : Harkrishan Lal Vasudeva
Publisher : Springer
Page : 522 pages
File Size : 46,5 Mb
Release : 2017-03-27
Category : Mathematics
ISBN : 9789811030208

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Elements of Hilbert Spaces and Operator Theory by Harkrishan Lal Vasudeva Pdf

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.

Author : Carlo Alabiso,Ittay Weiss
Publisher : Springer
Page : 267 pages
File Size : 49,5 Mb
Release : 2014-10-08
Category : Science
ISBN : 9783319037134

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A Primer on Hilbert Space Theory by Carlo Alabiso,Ittay Weiss Pdf

This book is an 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 an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

Author : Joseph Muscat
Publisher : Springer Nature
Page : 462 pages
File Size : 43,7 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9783031275371

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Functional Analysis by Joseph Muscat Pdf

Author : Vern I. Paulsen,Mrinal Raghupathi
Publisher : Cambridge University Press
Page : 193 pages
File Size : 47,7 Mb
Release : 2016-04-11
Category : Mathematics
ISBN : 9781107104099

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An Introduction to the Theory of Reproducing Kernel Hilbert Spaces by Vern I. Paulsen,Mrinal Raghupathi Pdf

A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.