On the Green Function and Poisson Integrals of the Dunkl Laplacian
| Autor: | Margit Rösler, Piotr Graczyk, Tomasz Luks |
|---|---|
| Přispěvatelé: | Laboratoire Angevin de Recherche en Mathématiques (LAREMA), Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS), Mathematisches Institut der Universität Paderborn, Graczyk, Piotr |
| Rok vydání: | 2017 |
| Předmět: |
Unit sphere
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR] Pure mathematics Rank (linear algebra) Mathematics::Number Theory Poisson kernel [MATH] Mathematics [math] Poisson distribution 01 natural sciences Potential theory 010104 statistics & probability symbols.namesake Mathematics - Analysis of PDEs Classical Analysis and ODEs (math.CA) FOS: Mathematics [MATH]Mathematics [math] 0101 mathematics Mathematics Newtonian potential Kernel (set theory) 010102 general mathematics [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Mathematics - Classical Analysis and ODEs symbols Primary 31B05 31B25 60J50 Secondary 42B30 51F15 Laplace operator Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Potential Analysis. 48:337-360 |
| ISSN: | 1572-929X 0926-2601 |
| DOI: | 10.1007/s11118-017-9638-6 |
| Popis: | We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian $\Delta_k$ in $\mathbb{R}^d$. As applications we derive the Poisson-Jensen formula for $\Delta_k$-subharmonic functions and Hardy-Stein identities for the Poisson integrals of $\Delta_k$. We also obtain sharp estimates of the Newton potential kernel, Green function and Poisson kernel in the rank one case in $\mathbb{R}^d$. These estimates contrast sharply with the well-known results in the potential theory of the classical Laplacian. Comment: 25 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink