Introduction To Hilbert Spaces With Applications

Author : Lokenath Debnath,Piotr Mikusinski
Publisher : Academic Press
Page : 600 pages
File Size : 47,6 Mb
Release : 2005-09-29
Category : Mathematics
ISBN : 9780122084386

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

"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.

Author : Lokenath Debnath,Piotr Mikusinski
Publisher : Elsevier
Page : 600 pages
File Size : 55,7 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 : Lokenath Debnath,Piotr Mikusiński
Publisher : Unknown
Page : 592 pages
File Size : 48,6 Mb
Release : 1999
Category : Mathematics
ISBN : UOM:39015045620864

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

The Second Edition of this successful text offers a systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis. It includes a simple introduction to the Lebesgue integral and a new chapter on wavelets. The book provides the reader with revised examples and updated diverse applications to differential and integral equations with clear explanations of these methods as applied to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation.

Author : N. Young
Publisher : Cambridge University Press
Page : 254 pages
File Size : 45,7 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 : Samuel S. Holland
Publisher : Courier Corporation
Page : 578 pages
File Size : 55,7 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 : N. Young
Publisher : Cambridge University Press
Page : 254 pages
File Size : 44,8 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 : Sterling K. Berberian
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 41,8 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 : W.-H. Steeb
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 50,5 Mb
Release : 2013-03-07
Category : Science
ISBN : 9789401153324

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Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics by W.-H. Steeb Pdf

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.

Author : Loknath
Publisher : Unknown
Page : 580 pages
File Size : 50,9 Mb
Release : 2005
Category : Hilbert space
ISBN : 8131201791

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Introduction To Hilbert Spaces With Applications, 3E by Loknath Pdf

Author : Harkrishan Lal Vasudeva
Publisher : Springer
Page : 522 pages
File Size : 51,5 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 : Joseph Muscat
Publisher : Springer Nature
Page : 462 pages
File Size : 42,9 Mb
Release : 2024-06-30
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 : 41,8 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.

Author : P.D. Hislop,I.M. Sigal
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461207412

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Introduction to Spectral Theory by P.D. Hislop,I.M. Sigal Pdf

The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.

Author : P.R. Halmos
Publisher : Springer Science & Business Media
Page : 385 pages
File Size : 42,9 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 : Gilbert Helmberg
Publisher : Elsevier
Page : 362 pages
File Size : 52,6 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.