Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse
Tom 184 / 2008
Studia Mathematica 184 (2008), 49-77
MSC: Primary 42A85, 30D60; Secondary 46E10, 47B38.
DOI: 10.4064/sm184-1-3
Streszczenie
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 ${\mathcal E}_{(\omega)} (\mathbb R)$.
