Bourbaki

Corollary 2

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

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

Let f:G→Hf: G\rightarrow H be a morphism of locally compact commutative topological groups. The morphism ff is strict if and only if f^\widehat{f} is strict.

In view of the canonical decomposition (E, II, p. 44) of a strict morphism, this follows from Lemmas 8 and 9.

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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Cites

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Machine translation of the English, by gpt-5.4, gpt-5-6-mini, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.