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Locally compact Abelian groups --- Measure theory

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Banach algebras --- Locally compact Abelian groups --- Algèbres normées. --- Analyse harmonique (mathématiques) --- Groupes abéliens localement compacts. --- Algèbres normées. --- Analyse harmonique (mathématiques) --- Groupes abéliens localement compacts.

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Groupes abéliens localement compacts. --- Fourier, Transformations de --- Locally compact Abelian groups. --- Fourier transformations. --- Algèbres de groupes --- Group algebras --- Analyse harmonique abstraite --- Analyse harmonique abstraite

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512.546 --- Topological groups --- 512.546 Topological groups --- Measure theory --- Mesure, Théorie de la --- Locally compact spaces --- Espaces localement compacts --- Représentations de groupes --- Representations of groups --- Groupes abéliens localement compacts --- Locally compact Abelian groups --- Measure theory. --- Mesure, Théorie de la --- Locally compact spaces. --- Représentations de groupes --- Representations of groups. --- Groupes abéliens localement compacts. --- Locally compact Abelian groups. --- Groupes topologiques --- Groupes compacts

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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

Harmonic analysis. --- Fourier analysis. --- Analysis, Fourier --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematical analysis --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Generalized Gelfand Pairs. --- Harmonic Analysis. --- Locally Compact Abelian Groups.