The convenient setting for ultradifferentiable mappings of Beurling- and Roumiue-type defined by a weight matrix

Abstract

We prove in a uniform way that all ultradifferentiable function classes of Roumieu- and of Beurling-type defined in terms of a weight matrix admit a convenient setting if the matrix satisfies some mild regularity conditions. We prove that these categories are cartesian closed and as special cases one obtains the classes defined by a weight sequence and by a weight function.

arXiv comment31 pages, this version is accepted for publication in the Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 22, issue 4, 2015