Real Algebraic and Analytic Geometry |

On two problems concerning quasianalytic Denjoy--Carleman classes.

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Submission: 2007, December 13.

*Abstract:
Given a Denjoy--Carleman class $Q=Q_{M}$, consider the Hilbert
space $H=H_{M}$ of some quasianalytic functions on the cube
$(-1,1)^{m}$, introduced by Thilliez~\cite{T}. In our
article~\cite{N}, we posed the question whether polynomials are
dense in $H$, and indicated that this open problem can be related
to that of certain decompositions of functions from $H$ with
respect to their Taylor series at zero, which is of great
geometric significance. In this paper we shall show that actually
the latter assertion entails the former.*

Mathematics Subject Classification (2000): 26E10.

Keywords and Phrases: quasianalytic functions, Sobolev spaces.

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