Corollary 1 (Orthogonality relations)

Tag 02JO, permanent. Cite it as [Bourbaki, Tag 02JO].

Théories spectrales, chapter II, § 1. Transformation de Fourier

Suppose G discrete and endowed with the counting measure. For $x$ and $y$ in G, one has

$\int$ 0 if $x\not=y$

\chi (x)\chi (y)d\chi =

$_{\widehat{G}}$ 1 if $x=y$ .

This results from the cor. to th. 1 of II, p. 215 and from duality.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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