2017
DOI: 10.1007/s10231-017-0649-0
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Solution to the first Cousin problem for vector-valued quasianalytic functions

Abstract: Abstract. We study spaces of vector-valued quasianalytic functions and solve the first Cousin problem in these spaces.

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Cited by 7 publications
(11 citation statements)
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“…for Ω convex this was proven by Rösner [18], whereas for general open sets Ω this was only recently shown by Vindas and the author [5]. Bonet and Domański proved (ii) by viewing -via the Fourier-Laplace transform (Ω is convex!)…”
Section: Introductionmentioning
confidence: 94%
“…for Ω convex this was proven by Rösner [18], whereas for general open sets Ω this was only recently shown by Vindas and the author [5]. Bonet and Domański proved (ii) by viewing -via the Fourier-Laplace transform (Ω is convex!)…”
Section: Introductionmentioning
confidence: 94%
“…Therefore, being the projective limit of a sequence of LB-spaces it follows that E {ω} (X) is webbed. It has been shown recently by Debrouwere and Vindas [DeVi,Proposition 3.2] that the space of ultradifferentiable functions of Roumieu type is ultrabornological.…”
Section: Spaces Of Ultradifferentiable Functionsmentioning
confidence: 99%
“…Due to the absence of nontrivial compactly supported quasianalytic functions the latter is much more difficult to establish than for Colombeau algebras of non-quasianalytic type. The proof is based on some of our recent results on the solvability of the Cousin problem for vector-valued quasianalytic functions [12]. We mention that the motivation for [12] was precisely this problem.…”
Section: Introductionmentioning
confidence: 99%
“…The proof is based on some of our recent results on the solvability of the Cousin problem for vector-valued quasianalytic functions [12]. We mention that the motivation for [12] was precisely this problem. In Section 5 we embed the infrahyperfunctions of class {M p } into our algebras and show that the multiplication of ultradifferentiable functions of class {M p } is preserved under the embedding we shall construct.…”
Section: Introductionmentioning
confidence: 99%