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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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##### References:
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