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

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Schmets J. , Valdivia M.

2005

tom 86

nr 3

227-243

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].

Extension maps in ultradifferentiable and ultraholomorphic function spaces

100%

Schmets J. , Valdivia M.

Studia Mathematica

2000

tom 143

nr 3

221-250

The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for $C^{∞}$-spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.