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Journal: Annales Mathematicae Silesianae

On energy formulas for symmetric semigroups

Farida Hmissi

Language: EN | Published: 30-09-2005 | Abstract | pp. 7-18

Let ℙ := (P_t)_t>o be a strongly continuous contraction semigroup of symmetric operators on L²(m). Let β be a Bochner subordinator and let ℙ^β be the subordinated semigroup of ℙ by means of β, i.e. P_t^β := ∫₀^∞ P_sβ_t(ds). We give in this paper an energy formula for the ℙ^β-potentials with finite energy in terms of the ℙ-exit laws and of β. We deduce an explicit energy formula for the α-potentials.

2005-09-30