Convolution with the kernel $e^{s\langle x\rangle^q}, q\geq 1, s>0$ 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 ≥ 1, s ∈ R\{0}.(R d ) (the ultradistributional analogue of the Schwartz space2010 Mathematics Subject Classification. 46F10 46F05. Key words and phrases. Convolution with exponentials, Gelfand-Shilov spaces, ultradistributions. B. Prangoski was partially supported by the bilateral project "Microlocal analysis and applications" funded by the Macedonian and Serbian academies of sciences and arts.