Titlebook: A First Course in Harmonic Analysis; Anton Deitmar Textbook 20021st edition Springer Science+Business Media New York 2002 Fourier analysis

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A First Course in Harmonic Analysis978-1-4757-3834-6Series ISSN 0172-5939 Series E-ISSN 2191-6675

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Akademisches Controlling an Hochschulenourier series and the Plancherel theorem for the real line. Therefore, it shows how abstract harmonic analysis indeed is a generalization of Fourier analysis. To be able to formulate the general Plancherel theorem for LCA groups we first need the notion of Haar integration.

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Malahat Wittmann,Kerstin Dübner-GeeThe theory of Fourier series is concerned with the question of whether a given periodic function, such as the plot of a heartbeat or the signal of a radio pulsar, can be written as a sum of simple waves. A . is described in mathematical terms as a function of the form . sin(2.) or . cos(2.) for an integer . and a complex number ..

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Malahat Wittmann,Kerstin Dübner-GeeIn this chapter we shall reinterpret the results of the previous one in terms of Hilbert spaces, since this is the appropriate setting for the generalizations of the results of Fourier theory, that will be given in the chapters to follow.

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