Remark 1

Tag 02K2, permanent. Cite it as [Bourbaki, Tag 02K2].

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

More generally, by the corollary to proposition 15 of II, p. 230, this formula is valid for every integrable complex function on $\mathbf{R}^n$ such that

\sum_{x\in\Lambda}|f(x+y)|<+\infty

for every $y\in \mathbf{R}^n$ and such that the function on $\mathbf{T}^n$ defined by

y\mapsto \sum_{x\in\Lambda}f(x+y)

is continuous and admits an absolutely convergent Fourier series (cf. below).

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.

Cited by

Nothing.

Cites

Nothing.