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

2023/04/20 by Chaabane Rejeb, Rejeb, Chaabane
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2304.10172

openalex publication_date 2023/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Δ_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 Δ_k-Dirichlet problem for annular regions. Secondly, we introduce and study the Δ_k-Green function of the annulus and we prove that it can be expressed by means of Δ_k-spherical harmonics. As applications, we obtain a Poisson-Jensen formula for Δ_k-subharmonic functions and we study positive continuous solutions for a Δ_k-semilinear problem.

Related

• On the Green function and Poisson integrals of the Dunkl Laplacian
• Potential kernels for radial Dunkl Laplacians
• The Neumann Green function of the annulus
• On the Green function of the annulus
• Uniform bounds on the Dunkl kernel