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

Annales Polonici Mathematici (2005)

- Volume: 86, Issue: 3, page 227-243
- ISSN: 0066-2216

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topJean 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 -

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