Explicit extension maps in intersections of non-quasi-analytic classes

Jean Schmets¹ ; Manuel Valdivia²

¹ Institut de Mathématique Université de Liège Sart Tilman Bât. B 37 B-4000 Liège 1, Belgium
² Facultad de Matemáticas Universidad de Valencia Dr. Moliner 50 E-46100 Burjasot (Valencia), Spain

Annales Polonici Mathematici, Tome 86 (2005) no. 3, pp. 227-243

Résumé

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}.

Détail

DOI : 10.4064/ap86-3-3

Keywords: projective limits classes functions prove chebyshev polynomials constitute absolute schauder basis nuclear chet spaces mathcal mathfrak there continuous linear extension map mit lambda mathfrak mathcal mathfrak mathbb under additional assumption mathfrak there explicit extension map mathcal mathfrak mathcal mathfrak modification chebyshev polynomials these results extend corresponding obtained beaugendre cite bth cite