Surjectivit� de l'application restriction � un compact dans des classes de fonctions ultradiff�rentiables

Chaumat, Jacques; Chollet, Anne-Marie

doi:10.1007/bf01459723

Cited by 56 publications

(107 citation statements)

References 5 publications

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“…(b) Let m = (m p ) p∈N 0 be an increasing sequence of real numbers such that m 0 = 1 and consider the sequence Chollet and Thilliez have made us aware that in fact the condition (A) implies the con- Therefore the main Theorem 1.1 leads to the following corollary to be compared with the results of [2]. (a) the condition ( * * ) holds;…”

Section: Some Information About the Sequences M And Mmentioning

confidence: 84%

“…Théorème 30 of [2] provides in particular the equivalence of the assertions (b) and (c) here above under stronger conditions on the sequences M 1 and M 2 . Commentaires 32 of [2] give a detailed discussion of the literature and ask for explicit constructions as well as for smoother conditions. In [4], one finds results similar to ours.…”

Section: Introductionmentioning

confidence: 85%

“…Lemma 4.1[2, Lemme 16]. Let (α k ) k∈N be a sequence of non-negative numbers such that ∞ k=1 α k < ∞.…”

mentioning

confidence: 98%

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On certain extension theorems in the mixed Borel setting

Schmets

Valdivia

2004

Journal of Mathematical Analysis and Applications

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Section: Some Information About the Sequences M And Mmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 85%

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On certain extension theorems in the mixed Borel setting

Schmets

Valdivia

2004

Journal of Mathematical Analysis and Applications

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“…M k ) follows from the following lemma, the statement and the proof of which is extracted from that of Proposition 17 of [1]. L e m m a 1.…”

Section: Ultradifferentiable Classesmentioning

confidence: 94%

Roots in differential rings of ultradifferentiable functions

Neelon

2007

Anal Math

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A b s t r a c t . Let {M k } be a logconvex sequence satisfying the differentiability condition sup(Mn+1/Mn) 1/n < ∞. It is shown that the Carleman class C{k! M k } contains all C ∞ roots of its nonflat elements, i.e., if f ∈ C{k! M k } and α > 0, thenIf {M k } also satisfies the additional condition M 1/n n → ∞, then the Beurling class C(k! M k ) is also contains all C ∞ roots of its nonflat elements.

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“…It also appears in [5]. The case * = {M n } can be found in [4], where the sequence M n , n = 0, 1, .…”

Section: Extensions Of Ultradifferentiable Functionsmentioning

confidence: 95%

On Whitney’s extension theorem for ultradifferentiable functions

Valdivia

2011

RACSAM

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Let M be a Whitney-regular bounded subset in the k-dimensional Euclidean space R k . We show in this article that certain jets of functions defined in the closure M of M are Whitney jets, either of Beurling type, or of Roumieu type, and as a consequence we give some results related with Whitney's extension theorem. We also obtain some structure theorems for ultradistributions T with support contained in a compact K , in terms of Borel measures concentrated at K .

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Surjectivit� de l'application restriction � un compact dans des classes de fonctions ultradiff�rentiables

Cited by 56 publications

References 5 publications

On certain extension theorems in the mixed Borel setting

On certain extension theorems in the mixed Borel setting

Roots in differential rings of ultradifferentiable functions

On Whitney’s extension theorem for ultradifferentiable functions

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