Contraction semigroups on $L_\infty({\bf R})$

Details Contraction semigroups on $L_\infty({\bf R})$ Contraction semigroups on $L_\infty({\bf R})$

2006-06-30

arxiv.org/abs/math/0606773v1

Mathematics

Analysis of PDEs

14 pages

Scientific paper

If $X$ is a non-degenerate vector field on ${\bf R}$ and $H=-X^2$ we examine
conditions for the closure of $H$ to generate a continuous semigroup on
$L_\infty$ which extends to the $L_p$-spaces. We give an example which cannot
be extended and an example which extends but for which the real part of the
generator on $L_2$ is not lower semibounded.

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