Geodesic
Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse
José Bonet 1   ; Reinhold Meise 2
1 IMPA-UPV and Dpto. de Matemática Aplicada Universidad Politécnica de Valencia E-46071 Valencia, Spain
2 Mathematisches Institut Heinrich-Heine-Universität Universitätsstrasse 1 40225 Düsseldorf, Germany
Studia Mathematica, Tome 184 (2008) no. 1, pp. 49-77 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space ${\mathcal E}_{(\omega)} (\mathbb R)$ of ($\omega$)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those ($\omega$)-ultradifferential operators which admit a continuous linear right inverse on ${\mathcal E}_{(\omega)} [a, b]$ for each compact interval $[a,b]$ and we show that this property is in fact weaker than the existence of a continuous linear right inverse on ${\mathcal E}_{(\omega)} (\mathbb R)$.
DOI : 10.4064/sm184-1-3
Keywords: extending previous work meise vogt characterize those convolution operators defined space mathcal omega mathbb omega quasianalytic functions beurling type variable which admit continuous linear right inverse characterize those omega ultradifferential operators which admit continuous linear right inverse mathcal omega each compact interval property weaker existence continuous linear right inverse mathcal omega mathbb

José Bonet  1   ; Reinhold Meise  2

1 IMPA-UPV and Dpto. de Matemática Aplicada Universidad Politécnica de Valencia E-46071 Valencia, Spain
2 Mathematisches Institut Heinrich-Heine-Universität Universitätsstrasse 1 40225 Düsseldorf, Germany 
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     title = {Characterization of the convolution operators
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José Bonet; Reinhold Meise. Characterization of the convolution operators
 on quasianalytic classes of Beurling type that admit a continuous linear right inverse. Studia Mathematica, Tome 184 (2008) no. 1, pp. 49-77. doi: 10.4064/sm184-1-3

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