Real Algebraic and Analytic Geometry |

Sums of squares in quasianalytic Denjoy-Carleman classes.

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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.:
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