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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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Keywords: $ {\text{LF}}$-space, constant coefficient linear partial differential operator, $ P$-convexity, strong $ P$-convexity
Article copyright: © Copyright 1970 American Mathematical Society

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