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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 \({\mathcal D}_{(\omega)}'(\Omega)\).

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
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