introduction to abstract harmonic analysis dover books on mathematics

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Introduction To Abstract Harmonic Analysis

Author : Lynn H. Loomis
ISBN : 9780486282312
Genre : Mathematics
File Size : 83. 49 MB
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Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.

A Course In Abstract Harmonic Analysis Second Edition

Author : Gerald B. Folland
ISBN : 9781498727150
Genre : Mathematics
File Size : 66. 2 MB
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A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant results and techniques that are of interest in their own right. This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its applications, and the book concludes with a more informal exposition on the theory of representations of non-Abelian, non-compact groups. Featuring extensive updates and new examples, the Second Edition: Adds a short section on von Neumann algebras Includes Mark Kac’s simple proof of a restricted form of Wiener’s theorem Explains the relation between SU(2) and SO(3) in terms of quaternions, an elegant method that brings SO(4) into the picture with little effort Discusses representations of the discrete Heisenberg group and its central quotients, illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular ones A Course in Abstract Harmonic Analysis, Second Edition serves as an entrée to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.

Fourier Analysis On Groups

Author : Walter Rudin
ISBN : 9780486821016
Genre : Mathematics
File Size : 35. 69 MB
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Written by a master mathematical expositor, this classic text reflects the results of the intense period of research and development in the area of Fourier analysis in the decade preceding its first publication in 1962. The enduringly relevant treatment is geared toward advanced undergraduate and graduate students and has served as a fundamental resource for more than five decades. The self-contained text opens with an overview of the basic theorems of Fourier analysis and the structure of locally compact Abelian groups. Subsequent chapters explore idempotent measures, homomorphisms of group algebras, measures and Fourier transforms on thin sets, functions of Fourier transforms, closed ideals in L1(G), Fourier analysis on ordered groups, and closed subalgebras of L1(G). Helpful Appendixes contain background information on topology and topological groups, Banach spaces and algebras, and measure theory.

Harmonic Analysis

Author : Carl L. DeVito
ISBN : 076373893X
Genre : Mathematics
File Size : 82. 28 MB
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Many branches of mathematics come together in harmonic analysis, each adding richness to the subject and each giving insights into this fascinating field. Devito's Harmonic Analysis presents a comprehensive introduction to Fourier analysis and Harmonic analysis and provides numerous examples and models so that students leave with a clear understanding of the theory.

Introduction To Analysis

Author : Maxwell Rosenlicht
ISBN : 0486650383
Genre : Mathematics
File Size : 54. 39 MB
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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition.

An Introduction To Harmonic Analysis

Author : Yitzhak Katznelson
ISBN : 0521543592
Genre : Mathematics
File Size : 57. 87 MB
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First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.

Harmonic Analysis On Homogeneous Spaces

Author : Nolan R. Wallach
ISBN : 0486816923
Genre : Harmonic analysis
File Size : 85. 50 MB
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Requiring background in linear algebra and advanced calculus, this text covers representation theory of compact Lie groups with applications to topology, geometry, and analysis and non-compact semi-simple Lie groups. 1973 edition.

An Introduction To Lebesgue Integration And Fourier Series

Author : Howard J. Wilcox
ISBN : 9780486137476
Genre : Mathematics
File Size : 38. 55 MB
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Undergraduate-level introduction to Riemann integral, measurable sets, measurable functions, Lebesgue integral, other topics. Numerous examples and exercises.

A First Course In Harmonic Analysis

Author : Anton Deitmar
ISBN : 9781475738346
Genre : Mathematics
File Size : 29. 17 MB
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This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.

Introductory Real Analysis

Author : A. N. Kolmogorov
ISBN : 0486612260
Genre : Mathematics
File Size : 58. 26 MB
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Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.

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