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

Derek W. Robinson·A. F. M. ter Elst
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Abstract

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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Derek W. Robinson, A. F. M. ter Elst. 2006-06-30. Contraction semigroups on $L_\infty({\bf R})$. https://arxiv.org/abs/math/0606773

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