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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0257689-0
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.
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Keywords:
<!– MATH ${\text {LF}}$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${\text {LF}}$">-space,
constant coefficient linear partial differential operator,
<IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$P$">-convexity,
strong <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img19.gif" ALT="$P$">-convexity
Article copyright:
© Copyright 1970
American Mathematical Society