arXiv subjects
Publications and source records attributed to Gerhard Schindl.
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.
We characterize stability under composition, inversion, and solution of ordinary differential equations for ultradifferentiable classes, and prove that all these stability properties are equivalent.
We characterize stability under composition of ultradifferentiable classes defined by weight sequences $M$, by weight functions $ω$, and, more generally, by weight matrices $\mathfrak{M}$, and investigate continuity of composition $(g,f) \mapsto f \circ g$. In addition, we represent the Beurling space $\mathcal{E}^{(ω)}$ and the Roumieu space $\mathcal{E}^{\{ω\}}$ as intersection and union of spaces $\mathcal{E}^{(M)}$ and $\mathcal{E}^{\{M\}}$ for associated weight sequences, respectively.