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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Solvability of differential equations with linear coefficients of nilpotent type
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by Rainer Felix PDF
Proc. Amer. Math. Soc. 94 (1985), 161-166 Request permission

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
  • © Copyright 1985 American Mathematical Society
  • 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