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Fourier series. --- Harmonic analysis. Fourier analysis --- 517.518.45 --- Fourier series --- 517.518.45 Fourier series

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Harmonic analysis. Fourier analysis --- 51 --- Mathematics --- Convergence. --- Fourier series. --- 51 Mathematics --- Fourier series --- Convergence --- Fourier, Séries de --- Convergence (mathématiques) --- Convergence (mathématiques) --- Fourier, Séries de --- Analyse harmonique

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Mathematical analysis --- 517.5 --- Theory of functions --- 517.5 Theory of functions --- Multipliers (Mathematical analysis) --- Multiplicateurs (analyse mathématique) --- Fourier series --- Convergence --- Fourier, Séries de --- Convergence (mathématiques) --- Fourier series. --- Convergence. --- Fourier, Séries de --- Convergence (mathématiques) --- Suites et series --- Sommabilite

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This book is concerned with the modern theory of Fourier series. Treating developments since Zygmund's classic study, the authors begin with a thorough discussion of the classical one-dimensional theory from a modern perspective. The text then takes up the developments of the 1970s, beginning with Fefferman's famous disc counterexample. The culminating chapter presents Cordoba's geometric theory of Kayeka maximal functions and multipliers. Research workers in the fields of Fourier analysis and harmonic analysis will find this a valuable account of these developments. Second year graduate students, who are familiar with Lebesgue theory and are acquainted with distributions, will be able to use this as a textbook which will bring them up to the exciting open questions in the field.

Fourier series. --- Convergence. --- Functions --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- Fourier series --- Convergence

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Number theory --- Automorphic forms. --- Fourier series. --- Nombres, Théorie des --- Formes automorphes --- Automorphic forms --- Number theory. --- Nombres, Théories des --- Fourier, Séries de