Bourbaki

Example

Tag 028A, permanent. Cite it as [Bourbaki, Tag 028A].

Théories spectrales, chapter I, § 3. Algèbres de Banach commutatives

Consider the Banach algebra A of absolutely convergent Fourier series (Example 4). Prop. 6, b), implies that if φ\varphi is a function on the unit circle U\mathbf{U} admitting an absolutely convergent Fourier series, and if φ\varphi does not vanish, the function 1/φ1/\varphi also admits an absolutely convergent Fourier series ("Wiener's theorem").

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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Machine translation of the English, by gpt-5.4, gpt-5-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.