Wyniki wyszukiwania

1

Extension maps in ultradifferentiable and ultraholomorphic function spaces

100%

Schmets J., Valdivia M.

Studia Mathematica

|

2000

|

tom 143

|

nr 3

221-250

EN

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.

2

The Zahorski theorem is valid in Gevrey classes

100%

Schmets J., Valdivia M.

Fundamenta Mathematicae

|

1996

|

tom 151

|

nr 2

149-166

EN

Let {Ω,F,G} be a partition of $ℝ^n$ such that Ω is open, F is $F_σ$ and of the first category, and G is $G_δ$. We prove that, for every γ ∈ ]1,∞[, there is an element of the Gevrey class Γγ which is analytic on Ω, has F as its set of defect points and has G as its set of divergence points.

3

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

100%

Schmets J., Valdivia M.

Annales Polonici Mathematici

|

2005

|

tom 86

|

nr 3

227-243

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].

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Fundamenta Mathematicae

1 Studia Mathematica

3 Schmets J.

3 Valdivia M.

1 2005

1 2000

1 1996

Extension maps in ultradifferentiable and ultraholomorphic function spaces

The Zahorski theorem is valid in Gevrey classes

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