Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type
Studia Mathematica, Tome 125 (1997) no. 2, pp. 101-129
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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.
@article{10_4064_sm_125_2_101_129,
author = {Thomas Meyer},
title = {Surjectivity of convolution operators on spaces of ultradifferentiable functions of {Roumieu} type},
journal = {Studia Mathematica},
pages = {101--129},
publisher = {mathdoc},
volume = {125},
number = {2},
year = {1997},
doi = {10.4064/sm-125-2-101-129},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-125-2-101-129/}
}
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%0 Journal Article %A Thomas Meyer %T Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type %J Studia Mathematica %D 1997 %P 101-129 %V 125 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-125-2-101-129/ %R 10.4064/sm-125-2-101-129 %G en %F 10_4064_sm_125_2_101_129
Thomas Meyer. Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type. Studia Mathematica, Tome 125 (1997) no. 2, pp. 101-129. doi: 10.4064/sm-125-2-101-129
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