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Solvability of differential equations with linear coefficients of nilpotent type


Author: Rainer Felix
Journal: Proc. Amer. Math. Soc. 94 (1985), 161-166
MSC: Primary 22E30; Secondary 22E25, 35A99, 46F99
DOI: https://doi.org/10.1090/S0002-9939-1985-0781075-9
MathSciNet review: 781075
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Abstract: Let $ L$ be the vector field on $ {{\mathbf{R}}^n}$ associated with a real nilpotent $ (n \times n)$-matrix. It is shown that $ L$ regarded as a differential operator defines a surjective mapping of the space $ \mathcal{S}'$ of tempered distributions onto itself; i.e. $ L\mathcal{S}'({{\mathbf{R}}^n}) = \mathcal{S}'({{\mathbf{R}}^n})$. Replacing $ \mathcal{S}'$ by the space $ \mathcal{D}'$ of ordinary distributions, this is not true in general.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0781075-9
Keywords: Divergences, invariant distributions, differential operators with critical points
Article copyright: © Copyright 1985 American Mathematical Society

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