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

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