On the range of convolution operators on non-quasianalytic ultradifferentiable functions. (English) Zbl 0918.46039
For a given weight function \(\omega: [0,\infty)\to [0,\infty)\) and an open set \(\Omega\subseteq \mathbb{R}^n\), the authors denote by \({\mathcal E}_{(\omega)}(\Omega)\) the non-quasianalytic class of Beurling type on \(\Omega\). They investigate conditions guaranteeing the surjectivity of the convolution operator \(T_\mu:{\mathcal E}_{(\omega)}(\Omega_1)\to {\mathcal E}_{(\omega)}(\Omega_2)\) for the given \(\mu\in{\mathcal E}_{(\omega)}'(\mathbb{R}^n)\). Analogous results are obtained also for ultradistributions of Roumieu type \({\mathcal D}_{(\omega)}'(\Omega)\).
Reviewer: L.Janos (Kent/Ohio)
MSC:
46F10 | Operations with distributions and generalized functions |
46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
46E10 | Topological linear spaces of continuous, differentiable or analytic functions |
35R50 | PDEs of infinite order |
46F15 | Hyperfunctions, analytic functionals |