Bourbaki

Remark

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

Théories spectrales, chapter V, § 3. Fonctions de type positif

Retain the notation of the proposition. It is possible that u(x1)u(x_1) is different from x2x_2 (exercise 3, b) of V, p. 493). However, the triplet (E2,u(x1),φ2)(E_2, u(x_1), \varphi_2) is also a Hilbert representation of λ\lambda.

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.