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

Jean Schmets; Manuel Valdivia

Annales Polonici Mathematici, Tome 85 (2005), p. 227-243 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 2005-01-01

Zbl 1106.26025

EUDML-ID : urn:eudml:doc:280468

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     year = {2005},
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Jean Schmets; Manuel Valdivia. Explicit extension maps in intersections of non-quasi-analytic classes. Annales Polonici Mathematici, Tome 85 (2005) pp. 227-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-3-3/