location:  Publications → journals → CMB
Abstract view

# Note on the Weierstrass Theorem in Quasianalytic Local Rings

Published:2013-10-14

Univ. Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
• Jean-Philippe Rolin,
Univ. de Bourgogne (Dijon), I.M.B., 9 av. A. Savary, BP47870, 21078 Dijon Cedex, France
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
 Format: LaTeX MathJax PDF

## Abstract

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.
 MSC Classifications: 26E10 - $C^\infty$-functions, quasi-analytic functions [See also 58C25] 26E05 - Real-analytic functions [See also 32B05, 32C05] 14P15 - Real analytic and semianalytic sets [See also 32B20, 32C05]