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Pré-Publication, Document De Travail Année : 2019

Green function and Poisson kernel associated to root systems for annular regions

Résumé

Let ∆ k be the Dunkl Laplacian relative to a fixed root system R in R d , d ≥ 2, and to a nonnegative multiplicity function k on R. Our first purpose in this paper is to solve the ∆ k-Dirichlet problem for annular regions. Secondly, we introduce and study the ∆ k-Green function of the annulus and we prove that it can be expressed by means of ∆ k-spherical harmonics. As applications, we obtain a Poisson-Jensen formula for ∆ k-subharmonic functions and we study positive continuous solutions for a ∆ k-semilinear problem.
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Dates et versions

hal-02005375 , version 1 (04-02-2019)

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  • HAL Id : hal-02005375 , version 1

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Chaabane Rejeb. Green function and Poisson kernel associated to root systems for annular regions. 2019. ⟨hal-02005375⟩
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