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

Volume 86 / 2005

Jean Schmets, Manuel Valdivia Annales Polonici Mathematici 86 (2005), 227-243 MSC: 26E10, 46E10. DOI: 10.4064/ap86-3-3


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}.


  • Jean SchmetsInstitut de Mathématique
    Université de Liège
    Sart Tilman Bât. B 37
    B-4000 Liège 1, Belgium
  • Manuel ValdiviaFacultad de Matemáticas
    Universidad de Valencia
    Dr. Moliner 50
    E-46100 Burjasot (Valencia), Spain

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