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Search: MSC category 26E10 ( $C^\infty$-functions, quasi-analytic functions [See also 58C25] )

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Parusiński, Adam; Rolin, Jean-Philippe
Note on the Weierstrass Theorem in Quasianalytic Local Rings
Consider quasianalytic local rings of germs of smooth functions closed under composition, implicit equation, and monomial division. We show that if the Weierstrass Preparation Theorem holds in such a ring then all elements of it are germs of analytic functions.

Categories:26E10, 26E05, 14P15

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