- Tytuł:
- Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type
- Autorzy:
- Meyer, Thomas
- Powiązania:
- https://bibliotekanauki.pl/articles/1219137.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- Let $ε_{{ω}}(I)$ denote the space of all ω-ultradifferentiable functions of Roumieu type on an open interval I in ℝ. In the special case ω(t) = t we get the real-analytic functions on I. For $μ ∈ ε_{{ω}}(I)'$ with $supp(μ) = {0}$ one can define the convolution operator $T_μ: ε_{{ω}}(I) → ε_{{ω}}(I)$, $T_μ(f)(x):= ⟨μ,f(x-·)⟩$. We give a characterization of the surjectivity of $T_μ$ for quasianalytic classes $ε_{{ω}}(I)$, where I = ℝ or I is an open, bounded interval in ℝ. This characterization is given in terms of the distribution of zeros of the Fourier Laplace transform $\widehat μ$ of μ.
- Źródło:
-
Studia Mathematica; 1997, 125, 2; 101-129
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł