Real Algebraic and Analytic Geometry
Submission: 2005, April 18.
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.
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