An Introduction to Hilbert Space


Author: N. Young
Publisher: Cambridge University Press
ISBN: 9780521337175
Category: Mathematics
Page: 239
View: 9413
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This textbook is an introduction to the theory of Hilbert spaces and its applications. The notion of a Hilbert space is a central idea in functional analysis and can be used in numerous branches of pure and applied mathematics. Dr. Young stresses these applications particularly for 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. The book is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). The book 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.

An Introduction to Hilbert Space


Author: N. Young
Publisher: Cambridge University Press
ISBN: 1107717167
Category: Mathematics
Page: 256
View: 3969
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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.

An Introduction to the Theory of Reproducing Kernel Hilbert Spaces


Author: Vern I. Paulsen,Mrinal Raghupathi
Publisher: Cambridge University Press
ISBN: 1107104092
Category: Mathematics
Page: 192
View: 9948
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A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.

Introduction to Hilbert Space


Author: Sterling K. Berberian
Publisher: American Mathematical Soc.
ISBN: 0821819127
Category: Mathematics
Page: 206
View: 8341
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Completely self-contained ... All proofs are given in full detail ... recommended for unassisted reading by beginners ... For teaching purposes this book is ideal. --Proceedings of the Edinburgh Mathematical Society The book is easy to read and, although the author had in mind graduate students, most of it is obviously appropriate for an advanced undergraduate course. It is also a book which a reasonably good student might read on his own. --Mathematical Reviews This textbook evolved from a set of course notes for first- or second-year graduate students in mathematics and related fields such as physics. It presents, in a self-contained way, various aspects of geometry and analysis of Hilbert spaces, including the spectral theorem for compact operators. Over 400 exercises provide examples and counter-examples for definitions and theorems in the book, as well as generalization of some material in the text. Aside from being an exposition of basic material on Hilbert space, this book may also serve as an introduction to other areas of functional analysis. The only prerequisite for understanding the material is a standard foundation in advanced calculus. The main notions of linear algebra, such as vector spaces, bases, etc., are explained in the first chapter of the book.

A Hilbert Space Problem Book


Author: P.R. Halmos
Publisher: Springer Science & Business Media
ISBN: 1468493302
Category: Mathematics
Page: 373
View: 3614
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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 Spectral Theory in Hilbert Space


Author: Gilbert Helmberg
Publisher: Courier Dover Publications
ISBN: 0486466221
Category: Mathematics
Page: 346
View: 2789
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This text introduces students to Hilbert space and bounded self-adjoint operators, as well as the spectrum of an operator and its spectral decomposition. The author, Emeritus Professor of Mathematics at the University of Innsbruck, Austria, has ensured that the treatment is accessible to readers with no further background than a familiarity with analysis and analytic geometry. Starting with a definition of Hilbert space and its geometry, the text explores the general theory of bounded linear operators, the spectral analysis of compact linear operators, and unbounded self-adjoint operators. Extensive appendixes offer supplemental information on the graph of a linear operator and the Riemann-Stieltjes and Lebesgue integration.

Linear Systems and Operators in Hilbert Space


Author: Paul A. Fuhrmann
Publisher: Courier Corporation
ISBN: 0486782263
Category: Mathematics
Page: 336
View: 5371
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Three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.

A Course in Modern Mathematical Physics

Groups, Hilbert Space and Differential Geometry
Author: Peter Szekeres
Publisher: Cambridge University Press
ISBN: 9780521829601
Category: Mathematics
Page: 600
View: 4128
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This book provides an introduction to the mathematics of modern physics, presenting concepts and techniques in mathematical physics at a level suitable for advanced undergraduates and beginning graduate students. It aims to introduce the reader to modern mathematical thinking within a physics setting. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book includes exercises and worked examples, to test the students' understanding of the various concepts, as well as extending the themes covered in the main text.

Reproducing Kernel Hilbert Spaces in Probability and Statistics


Author: Alain Berlinet,Christine Thomas-Agnan
Publisher: Springer Science & Business Media
ISBN: 1441990968
Category: Business & Economics
Page: 355
View: 2733
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The book covers theoretical questions including the latest extension of the formalism, and computational issues and focuses on some of the more fruitful and promising applications, including statistical signal processing, nonparametric curve estimation, random measures, limit theorems, learning theory and some applications at the fringe between Statistics and Approximation Theory. It is geared to graduate students in Statistics, Mathematics or Engineering, or to scientists with an equivalent level.

Linear Analysis

An Introductory Course
Author: Béla Bollobás
Publisher: Cambridge University Press
ISBN: 9780521655774
Category: Mathematics
Page: 240
View: 1377
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Revised and updated introduction to functional analysis.

Introduction to Banach Spaces and Algebras


Author: Graham R. Allan,Harold G. Dales
Publisher: Oxford University Press
ISBN: 0199206538
Category: Banach algebras
Page: 371
View: 2965
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A graduate level text in functional analysis, with an emphasis on Banach algebras. Based on lectures given for Part III of the Cambridge Mathematical Tripos, the text will assume a familiarity with elementary real and complex analysis, and some acquaintance with metric spaces, analytic topology and normed spaces (but not theorems depending on Baire category, or any version of the Hahn-Banach theorem).

Introduction to Operator Space Theory


Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 9780521811651
Category: Mathematics
Page: 478
View: 9452
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An introduction to the theory of operator spaces, emphasising applications to C*-algebras.

Introduction to Hilbert Spaces with Applications


Author: Lokenath Debnath,Piotr Mikusinski
Publisher: Elsevier
ISBN: 0080455921
Category: Mathematics
Page: 600
View: 2658
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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

Hilbert Space Methods in Signal Processing


Author: Rodney A. Kennedy,Parastoo Sadeghi
Publisher: Cambridge University Press
ISBN: 1107010039
Category: Mathematics
Page: 420
View: 1783
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An accessible introduction to Hilbert spaces, combining the theory with applications of Hilbert methods in signal processing.

Physical Mathematics


Author: Kevin Cahill
Publisher: Cambridge University Press
ISBN: 1107310733
Category: Science
Page: N.A
View: 2780
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Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.

Introduction to Model Spaces and their Operators


Author: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross
Publisher: Cambridge University Press
ISBN: 1107108748
Category: Mathematics
Page: 335
View: 7739
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A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.

Hilbert Space

Compact Operators and the Trace Theorem
Author: J. R. Retherford
Publisher: Cambridge University Press
ISBN: 9780521429337
Category: Mathematics
Page: 131
View: 1930
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The aim of this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory leading to an elementary proof of the Lidskij trace theorem. The author assumes the reader is familiar with linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach.

Lie Groups

An Introduction Through Linear Groups
Author: Wulf Rossmann
Publisher: Oxford University Press on Demand
ISBN: 9780199202515
Category: Mathematics
Page: 265
View: 3212
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Lie Groups is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of thetheory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

An Introduction to K-Theory for C*-Algebras


Author: M. Rørdam,Flemming Larsen,N. Laustsen
Publisher: Cambridge University Press
ISBN: 9780521789448
Category: Mathematics
Page: 242
View: 5866
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This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.