An Introduction to Hilbert Space

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Author: N. Young

Publisher: Cambridge University Press

ISBN: 9780521337175

Category: Mathematics

Page: 239

View: 3180

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 the Theory of Reproducing Kernel Hilbert Spaces

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Author: Vern I. Paulsen,Mrinal Raghupathi

Publisher: Cambridge University Press

ISBN: 1107104092

Category: Mathematics

Page: 192

View: 437

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

Introduction to Hilbert Spaces with Applications

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Author: Lokenath Debnath,Piotr Mikusinski

Publisher: Elsevier

ISBN: 0080455921

Category: Mathematics

Page: 600

View: 764

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

Introduction to Operator Space Theory

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Author: Gilles Pisier

Publisher: Cambridge University Press

ISBN: 9780521811651

Category: Mathematics

Page: 478

View: 807

An introduction to the theory of operator spaces, emphasising applications to C*-algebras.

A Course in Modern Mathematical Physics

Groups, Hilbert Space and Differential Geometry

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Author: Peter Szekeres

Publisher: Cambridge University Press

ISBN: 9780521829601

Category: Mathematics

Page: 600

View: 5881

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.

Linear Analysis

An Introductory Course

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Author: Béla Bollobás

Publisher: Cambridge University Press

ISBN: 9780521655774

Category: Mathematics

Page: 240

View: 8996

Revised and updated introduction to functional analysis.

Robust Control Theory in Hilbert Space

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Author: Avraham Feintuch

Publisher: Springer Science & Business Media

ISBN: 1461205913

Category: Mathematics

Page: 228

View: 7421

An operator theoretic approach to robust control analysis for linear time-varying systems, with the emphasis on the conceptual similarity with the H control theory for time-invariant systems. It clarifies the major difficulties confronted in the time varying case and all the necessary operator theory is developed from first principles, making the book as self-contained as possible. After presenting the necessary results from the theories of Toeplitz operators and nest algebras, linear systems are defined as input-output operators and the relationship between stabilisation and the existence of co-prime factorisations is described. Uniform optimal control problems are formulated as model-matching problems and are reduced to four block problems, while robustness is considered both from the point of view of fractional representations and the "time varying gap" metric, as is the relationship between these types of uncertainties. The book closes with the solution of the orthogonal embedding problem for time-varying contractive systems. As such, this book is useful to both mathematicians and to control engineers.

Wavelets

A Student Guide

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Author: Peter Nickolas

Publisher: Cambridge University Press

ISBN: 1316727939

Category: Mathematics

Page: N.A

View: 5063

This text offers an excellent introduction to the mathematical theory of wavelets for senior undergraduate students. Despite the fact that this theory is intrinsically advanced, the author's elementary approach makes it accessible at the undergraduate level. Beginning with thorough accounts of inner product spaces and Hilbert spaces, the book then shifts its focus to wavelets specifically, starting with the Haar wavelet, broadening to wavelets in general, and culminating in the construction of the Daubechies wavelets. All of this is done using only elementary methods, bypassing the use of the Fourier integral transform. Arguments using the Fourier transform are introduced in the final chapter, and this less elementary approach is used to outline a second and quite different construction of the Daubechies wavelets. The main text of the book is supplemented by more than 200 exercises ranging in difficulty and complexity.

Functional Analysis

An Elementary Introduction

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Author: Markus Haase

Publisher: American Mathematical Society

ISBN: 0821891715

Category: Mathematics

Page: 372

View: 8920

This book introduces functional analysis at an elementary level without assuming any background in real analysis, for example on metric spaces or Lebesgue integration. It focuses on concepts and methods relevant in applied contexts such as variational methods on Hilbert spaces, Neumann series, eigenvalue expansions for compact self-adjoint operators, weak differentiation and Sobolev spaces on intervals, and model applications to differential and integral equations. Beyond that, the final chapters on the uniform boundedness theorem, the open mapping theorem and the Hahn-Banach theorem provide a stepping-stone to more advanced texts. The exposition is clear and rigorous, featuring full and detailed proofs. Many examples illustrate the new notions and results. Each chapter concludes with a large collection of exercises, some of which are referred to in the margin of the text, tailor-made in order to guide the student digesting the new material. Optional sections and chapters supplement the mandatory parts and allow for modular teaching spanning from basic to honors track level.

Introduction to the Analysis of Normed Linear Spaces

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Author: J. R. Giles,John Robilliard Giles

Publisher: Cambridge University Press

ISBN: 9780521653756

Category: Mathematics

Page: 280

View: 2823

This text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. Giles illustrates the general theory with a great variety of example spaces.

Functional Analysis for Probability and Stochastic Processes

An Introduction

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Author: Adam Bobrowski

Publisher: Cambridge University Press

ISBN: 9781139443883

Category: Mathematics

Page: N.A

View: 6566

This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

An Introduction to Hankel Operators

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Author: Jonathan R. Partington

Publisher: Cambridge University Press

ISBN: 9780521367912

Category: Mathematics

Page: 103

View: 6680

Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.

Lineare Algebra

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Author: Gilbert Strang

Publisher: Springer-Verlag

ISBN: 3642556310

Category: Mathematics

Page: 656

View: 9183

Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

A Mathematical Introduction to Wavelets

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Author: P. Wojtaszczyk

Publisher: Cambridge University Press

ISBN: 9780521578943

Category: Mathematics

Page: 261

View: 7615

This book presents a mathematical introduction to the theory of orthogonal wavelets and their uses in analyzing functions and function spaces, both in one and in several variables. Starting with a detailed and self-contained discussion of the general construction of one dimensional wavelets from multiresolution analysis, the book presents in detail the most important wavelets: spline wavelets, Meyer's wavelets and wavelets with compact support. It then moves to the corresponding multivariable theory and gives genuine multivariable examples. The author discusses wavelet decompositions in Lp spaces, Hardy spaces and Besov spaces and provides wavelet characterizations of those spaces. Also included are periodic wavelets or wavelets not associated with a multiresolution analysis. This will be an invaluable book for those wishing to learn about the mathematical foundations of wavelets.

Hilbert Space Methods in Signal Processing

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Author: Rodney A. Kennedy,Parastoo Sadeghi

Publisher: Cambridge University Press

ISBN: 1107010039

Category: Mathematics

Page: 420

View: 9637

An accessible introduction to Hilbert spaces, combining the theory with applications of Hilbert methods in signal processing.

An Introduction to Harmonic Analysis on Semisimple Lie Groups

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Author: V. S. Varadarajan

Publisher: Cambridge University Press

ISBN: 9780521663625

Category: Mathematics

Page: 316

View: 4365

Now in paperback, this graduate-level textbook is an excellent introduction to the representation theory of semi-simple Lie groups. Professor Varadarajan emphasizes the development of central themes in the context of special examples. He begins with an account of compact groups and discusses the Harish-Chandra modules of SL(2,R) and SL(2,C). Subsequent chapters introduce the Plancherel formula and Schwartz spaces, and show how these lead to the Harish-Chandra theory of Eisenstein integrals. The final sections consider the irreducible characters of semi-simple Lie groups, and include explicit calculations of SL(2,R). The book concludes with appendices sketching some basic topics and with a comprehensive guide to further reading. This superb volume is highly suitable for students in algebra and analysis, and for mathematicians requiring a readable account of the topic.

An Introduction to Nonlinear Analysis

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Author: Martin Schechter

Publisher: Cambridge University Press

ISBN: 9780521843973

Category: Mathematics

Page: 357

View: 2974

The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.

Introduction to Banach Spaces and Algebras

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Author: Graham R. Allan,Harold G. Dales

Publisher: Oxford University Press

ISBN: 0199206538

Category: Banach algebras

Page: 371

View: 921

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).

Geometry of Quantum States

An Introduction to Quantum Entanglement

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Author: Ingemar Bengtsson,Karol Życzkowski

Publisher: Cambridge University Press

ISBN: 1108293492

Category: Science

Page: N.A

View: 4559

Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.