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

TL;DR

This paper establishes a unified framework for ultradifferentiable function classes defined by weight matrices, showing they are cartesian closed under mild conditions, thus enabling advanced functional analysis techniques.

Contribution

It provides a uniform proof that ultradifferentiable classes of Roumieu- and Beurling-type defined by weight matrices admit a convenient setting, generalizing previous results.

Findings

Ultradifferentiable classes are cartesian closed under mild regularity conditions.

The framework includes classes defined by weight sequences and functions as special cases.

The results facilitate functional analysis in ultradifferentiable function spaces.

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.