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Dijk, Gerrit van

Introduction to Harmonic Analysis and Generalized Gelfand Pairs

Series:De Gruyter Studies in Mathematics 36

    94,95 € / $133.00 / £86.50*

    eBook (PDF)
    Publication Date:
    December 2009
    Copyright year:
    2009
    ISBN
    978-3-11-022020-9
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    Overview

    Aims and Scope

    This book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed.

    This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space.

    From the contents

    • Fourier series
    • Fourier integrals
    • Locally compact groups
    • Haar measures
    • Harmonic analysis on locally compact abelian groups
    • Theory and examples of Gelfand pairs
    • Theory and examples of generalized Gelfand pairs

    Details

    ix, 223 pages
    Language:
    English
    Type of Publication:
    Monograph
    Keyword(s):
    Harmonic Analysis; Generalized Gelfand Pairs; Locally Compact Abelian Groups

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    Gerrit van Dijk, Leiden University, Netherlands

    Reviews

    "The book under review is basically self-contained, only requiring basic functional analysis, some knowledge of distribution theory and elementary Lie theory. The material presented in the book is carefully explained so that it can be used for self-study." Mathematical Reviews

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