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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A closed subspace of $ \mathcal{D}(\Omega)$ which is not an $ \mathrm{LF}$-space


Authors: M. J. Kascic and B. Roth
Journal: Proc. Amer. Math. Soc. 24 (1970), 801-802
MSC: Primary 46.01; Secondary 35.00
MathSciNet review: 0257689
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Abstract: With proper choice of region $ \Omega \subseteq {R^n}$ and constant coefficient linear partial differential operator $ P$, namely $ \Omega $ being $ P$-convex but not strong $ P$-convex, the range of $ P$ in $ \mathcal{D}(\Omega )$ is a closed subspace of $ \mathcal{D}(\Omega )$ whose subspace topology differs from its canonical $ {\text{LF}}$-topology. In the present paper this result is proved and an example of a pair $ \Omega ,\;P$ satisfying the above hypotheses is presented.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0257689-0
PII: S 0002-9939(1970)0257689-0
Keywords: $ {\text{LF}}$-space, constant coefficient linear partial differential operator, $ P$-convexity, strong $ P$-convexity
Article copyright: © Copyright 1970 American Mathematical Society