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.
KeywordsFourier Series Compact Group Complex Vector Space Left Translation Simultaneous Generalization
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