Journal article
Compact symmetry groups and generators for sub-Markovian semigroups
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol.63(1), pp.17-27
03/1983
DOI: 10.1007/BF00534173
Abstract
We consider closed infinitesimal operators L with dense domain D in the algebra of all continuous functions, vanishing at infinity, on a given locally compact Hausdorff space X. Necessary and sufficient conditions are given for L to be the infinitesimal generator of a strongly continuous sub-Markovian semigroup on C 0(X). The conditions involve: (1) commutativity with a compact group G acting continuously on X (i.e., spatial G-symmetry), (2) a tangential notion defined in terms of the G-action, and finally, (3) a dispersive estimate for L. The dispersive estimate is satisfied on a subalgebra which is a core for L, and contained in the domain D. If G is also a Lie group, we explicitly construct such a core algebra in the domain.
Details
- Title: Subtitle
- Compact symmetry groups and generators for sub-Markovian semigroups
- Creators
- Palle E. T Jørgensen
- Resource Type
- Journal article
- Publication Details
- Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol.63(1), pp.17-27
- DOI
- 10.1007/BF00534173
- ISSN
- 0044-3719
- eISSN
- 1432-2064
- Language
- English
- Date published
- 03/1983
- Academic Unit
- Mathematics
- Record Identifier
- 9983985839602771
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