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Auteur : Gerald B. Folland
Catégorie : Livres anglais et étrangers,Science,Mathematics
Broché : * pages
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Langue : Français, Anglais

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.

Télécharger A Course in Abstract Harmonic Analysis de Gerald B. Folland Livres Pdf Epub

A Course in Abstract Harmonic Analysis ~ vi A Course in Abstract Harmonic Analysis oremt, ia these books are used freely here, often without any specific refereat:e: Rudin [108] also contains most of the material in Chapter 1, but the latter is included here because some of the concepts in it - especially projection-valued measures and the Gelfand transform - are an essential part of the fabric of ideas in later sections, and because .

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Abstract Harmonic Analysis / SpringerLink ~ Abstract Harmonic Analysis Volume I, Structure of Topological Groups Integration theory Group Representations. Authors (view affiliations) Edwin Hewitt; Kenneth A. Ross; Book. 123 Citations; 2.2k Downloads; Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GMW) Log in to check access . Buy eBook. USD 84.99 Instant download; Readable on all devices; Own it forever .

A Course in Harmonic Analysis - scholarsmine.mst.edu ~ In Chapter 4, we present a survey of results in abstract Fourier trans-form, relying primarily on the textbook of Folland [9]. In particular, we demonstrate how many of the preceding topics may be viewed un-der the same umbrella (i.e. Fourier analysis on locally compact abelian groups). Most results are stated without proof. We then brie y discuss the case of Fourier analysis on compact groups .

A First Course in Harmonic Analysis - GBV ~ A First Course in Harmonic Analysis Springer. Contents I Fourier Analysis 1 1 Fourier Series 3 1.1 Periodic Functions 3 1.2 Exponentials 5 1.3 The Bessel Inequality 7 1.4 Completeness in the L2-Norm 8 1.5 Uniform Convergence of Fourier Series 14 1.6 Periodic Functions Revisited 16 1.7 Exercises 17 2 Hilbert Spaces 21 2.1 Pre-Hilbert and Hilbert Spaces 21 2.2 ^-Spaces 25 2.3 Orthonormal Bases .

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A Course in Abstract Harmonic Analysis / Taylor & Francis ~ 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 resul . TABLE OF CONTENTS . chapter 1 / 34 pages .

A Course in Abstract Harmonic Analysis (Studies in ~ "A Course in Abstract Harmonic Analysis" offers a concise, readable introduction to Fourier analysis on groups and unitary representation theory.After a brief review of the relevant parts of Banach algebra theory and spectral theory, the book proceeds to the basic facts about locally compact groups, Haar measure, and unitary representations, including the Gelfand-Raikov existence theorem. The .

A course in abstract harmonic analysis (Book, 1995 ~ Despite this, however, there are few, if any introductory texts that present a unified picture of the general abstract theory.\/span>\"@ en\/a> ; \n schema:description\/a> \" A Course in Abstract Harmonic Analysis offers a concise, readable introduction to Fourier analysis on groups and unitary representation theory. After a brief review of the relevant parts of Banach .

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A Course in Harmonic Analysis - Missouri S&T ~ In Chapter 4, we present a survey of results in abstract Fourier trans-form, relying primarily on the textbook of Folland [9]. In particular, we demonstrate how many of the preceding topics may be viewed un-der the same umbrella (i.e. Fourier analysis on locally compact abelian groups). Most results are stated without proof. We then brie y discuss the case of Fourier analysis on compact groups .

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Introduction to Abstract Harmonic Analysis for ~ A second book you should look at is Folland's "A Course in Abstract Harmonic Analysis", which is more advanced, and requires more experience with analysis (having seen Banach spaces is not a bad thing), but the advantage of this book is that it has very clearly written proofs, that are easily to follow (I do algebra mostly, and I find many analysis tracts a bit opaque in this regard .

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Abstract Harmonic Analysis / SpringerLink ~ Abstract Harmonic Analysis Volume II: Structure and Analysis for Compact Groups Analysis on Locally Compact Abelian Groups. Authors (view affiliations) Edwin Hewitt; Kenneth A. Ross; Book. 44 Citations; 3.4k Downloads; Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 152) Log in to check access . Buy eBook. USD 109.00 Instant download; Readable on all devices .

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