Contraction Semigroups on L ∞(R)

Antonius F. M. ter Elst () and Derek W. Robinson ()
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Antonius F. M. ter Elst: University of Auckland, Department of Mathematics
Derek W. Robinson: Australian National University, Centre for Mathematics and its Applications Mathematical Sciences Institute

A chapter in Functional Analysis and Evolution Equations, 2007, pp 209-221 from Springer

Abstract: Abstract If X is a non-degenerate derivation on R and H = −X 2 we examine conditions for the closure of H to generate a weakly* continuous semigroup on L ∞ 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.

Keywords: Contraction semigroup; dissipative operator; derivation; sum of squares of vector fields (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7794-6_14

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DOI: 10.1007/978-3-7643-7794-6_14

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