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Continuous linear right inverses for partial differential operators on non-quasianalytic classes and on ultradistributions. (English) Zbl 0858.46030
Summary: Characterizations are given of those linear partial differential operators with constant coefficients which admit a continuous linear right inverse on \({\mathcal E}_{(\omega)}(\Omega)\) (resp. \({\mathcal E}_{\{\omega\}}(\Omega)\)) and/or \({\mathcal D}_{(\omega)}'(\Omega)\) (resp. \({\mathcal D}_{\{\omega\}}(\Omega)\)), where \(\Omega\) is an open set in \(\mathbb{R}^n\). The characterizations are in the same spirit as in the previous results of the authors on the existence of right inverses on \(C^\infty(\Omega)\) and/or \({\mathcal D}'(\Omega)\).

MSC:
46F05 Topological linear spaces of test functions, distributions and ultradistributions
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
32U05 Plurisubharmonic functions and generalizations
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