On energy formulas for symmetric semigroups
Abstract
Let ℙ := (Pt)t>o be a strongly continuous contraction semigroup of symmetric operators on L2(m). Let β be a Bochner subordinator and let ℙβ be the subordinated semigroup of ℙ by means of β, i.e. Ptβ := ∫0∞ Psβt(ds). We give in this paper an energy formula for the ℙβ-potentials with finite energy in terms of the ℙ-exit laws and of β. We deduce an explicit energy formula for the α-potentials.
Keywords
symmetric semigroup; potential; energy; exit law; Bochner subordination
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Départment de Mathématiques, Faculté des Sciences de Tunis, Tunisia Tunisia
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