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
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 ${\mathcal E}_{(\omega)} (\mathbb R)$.
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
Affiliations des auteurs :
José Bonet 1 ; Reinhold Meise 2
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author = {Jos\'e Bonet and Reinhold Meise},
title = {Characterization of the convolution operators
on quasianalytic classes of {Beurling} type that admit a continuous linear right inverse},
journal = {Studia Mathematica},
pages = {49--77},
publisher = {mathdoc},
volume = {184},
number = {1},
year = {2008},
doi = {10.4064/sm184-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm184-1-3/}
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%0 Journal Article %A José Bonet %A Reinhold Meise %T Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse %J Studia Mathematica %D 2008 %P 49-77 %V 184 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm184-1-3/ %R 10.4064/sm184-1-3 %G en %F 10_4064_sm184_1_3
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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