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

Jean Schmets, and Manuel Valdivia. "Explicit extension maps in intersections of non-quasi-analytic classes." Annales Polonici Mathematici 86.3 (2005): 227-243. <http://eudml.org/doc/280468>.

@article{JeanSchmets2005,
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 $_\{()\}([-1,1]^r)$; (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].},
author = {Jean Schmets, Manuel Valdivia},
journal = {Annales Polonici Mathematici},
keywords = {Schauder bases},
language = {eng},
number = {3},
pages = {227-243},
title = {Explicit extension maps in intersections of non-quasi-analytic classes},
url = {http://eudml.org/doc/280468},
volume = {86},
year = {2005},
}

TY - JOUR
AU - Jean Schmets
AU - Manuel Valdivia
TI - Explicit extension maps in intersections of non-quasi-analytic classes
JO - Annales Polonici Mathematici
PY - 2005
VL - 86
IS - 3
SP - 227
EP - 243
AB - 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].
LA - eng
KW - Schauder bases
UR - http://eudml.org/doc/280468
ER -