Pré-Publication, Document De Travail Année : 2019

Potential kernels for radial Dunkl Laplacians

T Luks
  • Fonction : Auteur
  • PersonId : 1056183

Résumé

We derive two-sided bounds for the Newton and Poisson kernels of the W-invariant Dunkl Laplacian in geometric complex case when the multiplicity k(α) = 1 i.e. for flat complex symmetric spaces. For the invariant Dunkl-Poisson kernel P W (x, y), the estimates are P W (x, y) P R d (x, y) α>0 |x − σ α y| 2k(α) , where the α's are the positive roots of a root system acting in R d , the σ α 's are the corresponding symmetries and P R d is the classical Poisson kernel in R d. Analogous bounds are proven for the Newton kernel when d ≥ 3. The same estimates are derived in the rank one direct product case Z N 2 and conjectured for general W-invariant Dunkl processes. As an application, we get a two-sided bound for the Poisson and Newton kernels of the classical Dyson Brownian motion and of the Brownian motions in any Weyl chamber.

Fichier principal
Vignette du fichier
PGTLPS.pdf (389.42 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence
Loading...

Dates et versions

hal-02318902 , version 1 (17-10-2019)

Licence

Identifiants

  • HAL Id : hal-02318902 , version 1

Citer

Piotr Graczyk, T Luks, P Sawyer. Potential kernels for radial Dunkl Laplacians. 2019. ⟨hal-02318902⟩
87 Consultations
378 Téléchargements

Partager

  • More