Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse

José Bonet, and Reinhold Meise. "Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse." Studia Mathematica 184.1 (2008): 49-77. <http://eudml.org/doc/284390>.

@article{JoséBonet2008,
abstract = {Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space $_\{(ω)\}(ℝ)$ of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on $_\{(ω)\} [a, b]$ 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 $_\{(ω)\}(ℝ)$.},
author = {José Bonet, Reinhold Meise},
journal = {Studia Mathematica},
keywords = {Fourier-Laplace transform; property (DN)},
language = {eng},
number = {1},
pages = {49-77},
title = {Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse},
url = {http://eudml.org/doc/284390},
volume = {184},
year = {2008},
}

TY - JOUR
AU - José Bonet
AU - Reinhold Meise
TI - Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse
JO - Studia Mathematica
PY - 2008
VL - 184
IS - 1
SP - 49
EP - 77
AB - Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space $_{(ω)}(ℝ)$ of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on $_{(ω)} [a, b]$ 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 $_{(ω)}(ℝ)$.
LA - eng
KW - Fourier-Laplace transform; property (DN)
UR - http://eudml.org/doc/284390
ER -