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Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse. (English) Zbl 0703.46025
Solving a problem of L. Schwartz, those constant coefficient partial differential operators P(D) are characterized that admit a continuous linear right inverse on \({\mathcal E}(\Omega)\) or \({\mathcal D}'(\Omega)\), \(\Omega\) an open set in \({\mathbb{R}}^ n\). For bounded \(\Omega\) with \(C^ 1\)-boundary these properties are equivalent to P(D) being very hyperbolic. For \(\Omega ={\mathbb{R}}^ n\) they are equivalent to a Phragmén-Lindelöf condition holding on the zero variety of the polynomial P.
Reviewer: R.Meise

MSC:
46F10 Operations with distributions and generalized functions
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
47F05 General theory of partial differential operators
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