Explicit extension maps in intersections of non-quasi-analytic classes
Volume 86 / 2005
Annales Polonici Mathematici 86 (2005), 227-243
MSC: 26E10, 46E10.
DOI: 10.4064/ap86-3-3
Abstract
We deal with projective limits of classes of functions and prove that: (a) the Chebyshev polynomials constitute an absolute Schauder basis of the nuclear Fréchet spaces ${\mathcal E}_{(\mathfrak M)}{([-1,1]^r)}$; (b) there is no continuous linear extension map from ${\mit\Lambda}^{(r)}_{(\mathfrak M)}$ into $\mathcal{B}_{(\mathfrak M)}{(\mathbb R^r)}$; (c) under some additional assumption on $\mathfrak M$, there is an explicit extension map from ${\mathcal E}_{(\mathfrak M)}{([-1,1]^r)}$ into $\mathcal{D}_{(\mathfrak M)}{([-2,2]^r)}$ by use of a modification of the Chebyshev polynomials. These results extend the corresponding ones obtained by Beaugendre in \cite{BTh} and \cite{B}.
