Compact symmetry groups and generators for sub-Markovian semigroups

  • Palle E. T. Jørgensen


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 C0(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.


Continuous Function Stochastic Process Probability Theory Symmetry Group Mathematical Biology 
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© Springer-Verlag 1983

Authors and Affiliations

  • Palle E. T. Jørgensen
    • 1
  1. 1.Department of Mathematics ElUniversity of PennsylvaniaPhiladelphiaUSA

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