Real Algebraic and Analytic Geometry Preprint Server

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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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