Bourbaki

Corollary

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

Théories spectrales, chapter I, § 4. Calcul fonctionnel holomorphe

Assume that A is nonzero. Let a∈Cn⊂An\boldsymbol{a}\in \mathbf{C}^n\subset A^n. One has SpAn(a)={a}^n_A(\boldsymbol{a}) =\{\boldsymbol{a}\}. For every germ f∈O({a};A)f\in \mathscr{O}(\{\boldsymbol{a}\}; A), one has Θa(f)=f(a)\Theta_{\boldsymbol{a}}(f) =f(\boldsymbol{a}).

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-5-6-mini, gpt-5-mini, gpt-5.4, 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.