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

• Autorzy: Jean Schmets , Manuel Valdivia
• Języki publikacji: EN

Abstrakty

EN

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 $𝓔_{(𝔐)}([-1,1]^r)$; (b) there is no continuous linear extension map from $Λ^{(r)}_{(𝔐)}$ into $𝓑_{(𝔐)}(ℝ^r)$; (c) under some additional assumption on 𝔐, there is an explicit extension map from $𝓔_{(𝔐)}([-1,1]^r)$ into $𝓓_{(𝔐)}([-2,2]^r)$ by use of a modification of the Chebyshev polynomials. These results extend the corresponding ones obtained by Beaugendre in [1] and [2].

Kategorie tematyczne

• 46E10: Topological linear spaces of continuous, differentiable or analytic functions
• 26E10: C ∞ -functions, quasi-analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2005
• Tom: 86
• Numer: 3
• Strony: 227-243

Daty

wydano

2005

Twórcy

autor

Jean Schmets

• Institut de Mathématique, Université de Liège, Sart Tilman Bât. B 37, B-4000 Liège 1, Belgium

autor

Manuel Valdivia

• Facultad de Matemáticas, Universidad de Valencia, Dr. Moliner 50, E-46100 Burjasot (Valencia), Spain

Identyfikatory

DOI

10.4064/ap86-3-3