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## Annales Polonici Mathematici

2014 | 111 | 1 | 13-20
Tytuł artykułu

### On a problem concerning quasianalytic local rings

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Języki publikacji
EN
Abstrakty
EN
Let (𝓒ₙ)ₙ be a quasianalytic differentiable system. Let m ∈ ℕ. We consider the following problem: let $f ∈ 𝓒_{m}$ and f̂ be its Taylor series at $0 ∈ ℝ^{m}$. Split the set $ℕ^{m}$ of exponents into two disjoint subsets A and B, $ℕ^{m} = A ∪ B$, and decompose the formal series f̂ into the sum of two formal series G and H, supported by A and B, respectively. Do there exist $g,h ∈ 𝓒_{m}$ with Taylor series at zero G and H, respectively? The main result of this paper is the following: if we have a positive answer to the above problem for some m ≥ 2, then the system (𝓒ₙ)ₙ is contained in the system of analytic germs. As an application of this result, we give a simple proof of Carleman's theorem (on the non-surjectivity of the Borel map in the quasianalytic case), under the condition that the quasianalytic classes considered are closed under differentiation, for n ≥ 2.
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Kategorie tematyczne
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Rocznik
Tom
Numer
Strony
13-20
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
• Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, BP 133 Kénitra, Maroc
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