Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2005, April 18.

Abstract:
We show that a nonnegative function germ at the origin of $\R ^2$ belonging to a quasianalytic Denjoy-Carleman class can be written as a sum of two squares of functions which lie in a Denjoy-Carleman class again. When the germ is elliptic we prove that the class is the same, in the general case a loss of regularity is possible.

Mathematics Subject Classification (2000): 26E10, 14P15, 11E25.

Keywords and Phrases: Quasianalytic, Denjoy-Carleman class, sum of squares.

Full text, 26p.: dvi 127k, ps.gz 199k, pdf 253k.