Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces

We introduce and study a number of new spaces of ultradifferentiable functions and ultradistributions and we apply our results to the study of the convolution of ultradistributions. The spaces of convolutors O-C'*(R-d) for tempered ultradistributions are analyzed via the duality with respect to the test function spaces O-C*(R-d) introduced in this article. We also study ultradistribution spaces associated to translation-invariant Banach spaces of tempered ultradistributions and use their properties to provide a full characterization of the general convolution of Roumieu ultradistributions via the space of integrable ultradistributions. We show that the convolution of two Roumieu ultra distributions T, S is an element of D'({Mp}) (R-d) exists if and only if (phi * S)T is an element of D-L1'({Mp}) (R-d) for every phi is an element of D-{Mp} (R-d).

Jaar van publicatie:2016

BOF-keylabel:ja

IOF-keylabel:ja

BOF-publication weight:0.1

CSS-citation score:2

Auteurs:International

Authors from:Higher Education

Toegankelijkheid:Open