Convolution with the kernel $e^{s⟨x{⟩}^q},q\ge 1,s>0$ within ultradistribution spaces

Abstract

We consider the existence of convolution of Roumieu type ultradistribution with the kernel $e^{s(1+|x{|}^2{)}^{q/2}},q\ge 1$, $s\in\RR\backslash\{0\}$.