Bourbaki

Definition 5

Tag 03B5, permanent. Cite it as [Bourbaki, Tag 03B5].

Théories spectrales, chapter V, § 2. Représentations des groupes localement compacts

Let ϱ\varrho be a unitary representation of R\mathbf{R} in E. The symmetric partial operator defined in Lemma 12 is called the infinitesimal generator of ϱ\varrho.

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

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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.