Abstract
In this chapter the general Plancherel theorem will be given. The general Plancherel theorem is a simultaneous generalization of the completeness of Fourier 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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© 2002 Springer Science+Business Media New York
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Deitmar, A. (2002). Plancherel Theorem. In: A First Course in Harmonic Analysis. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3834-6_7
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DOI: https://doi.org/10.1007/978-1-4757-3834-6_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3836-0
Online ISBN: 978-1-4757-3834-6
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