The Plancherel theorem reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Plancherel theorem

In mathematics, the Plancherel theorem is a result in harmonic analysis, first proved by Michel Plancherel. It states that if a function f is in both L¹ and L², then its Fourier transform is in L². The Fourier transform map actually extends from L¹∩L²→L² to an isomorphism L²→L².

Here Plancherel's version applied to functions on the real line. The theorem is valid in abstract versions, on locally compact abelian groups in general.

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