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Topological groups. Lie groups --- Category theory. Homological algebra --- 512.73 --- Cohomology theory of algebraic varieties and schemes --- 512.73 Cohomology theory of algebraic varieties and schemes --- Group theory. --- Homology theory. --- Groupes, Théorie des. --- Cohomologie. --- Groupes abéliens localement compacts --- Locally compact Abelian groups --- Groupes, Théorie des --- Cohomologie --- Groupes abéliens localement compacts. --- Locally compact Abelian groups. --- Abelian groups. --- Groupes topologiques --- Groupes compacts
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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.
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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. --- Groupes topologiques --- Groupes compacts --- Groupes topologiques --- Groupes compacts
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