On energy formulas for symmetric semigroups

Farida Hmissi

Published: 2005-09-30

Vol. 19 (2005)

On energy formulas for symmetric semigroups

Farida Hmissi

Abstract

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.

Keywords:

symmetric semigroup , potential , energy , exit law , Bochner subordination

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Hmissi, F. (2005). On energy formulas for symmetric semigroups. Annales Mathematicae Silesianae, 19, 7–18. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14079

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Vol. 19 (2005)
Published: 2005-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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