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Pré-Publication, Document De Travail Année : 2016

Newtonian potentials and subharmonic functions associated to root systems

Résumé

The purpose of this paper is to present a new theory of subharmonic functions for the Dunkl-Laplace operator ∆ k in R d associated to a root system and a multiplicity function k ≥ 0. In particular, we introduce and study a Dunkl-Newton kernel and the corresponding potential of Radon measures. As applications we give a strong maximum principle, a solution of the Poisson equation and a Riesz decomposition theorem for ∆ k-subharmonic functions.
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Dates et versions

hal-01368871 , version 1 (20-09-2016)

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  • HAL Id : hal-01368871 , version 1

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Léonard Gallardo, Chaabane Rejeb. Newtonian potentials and subharmonic functions associated to root systems. 2016. ⟨hal-01368871⟩
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