6 citations · 10 across the 11 of their papers we have counts for
12 papers
A reduction formula for the Dunkl kernel for the root systems of type
P. Sawyer
In this paper, we provide a reduction formula for the Dunkl kernel for the root systems of type . The Dunkl kernel for the root system is expressed as an integral involvin…
A formula and sharp estimates for the Dunkl kernel for the root system
P. Graczyk, P. Sawyer
In this paper, we transform a formula for the Dunkl kernel by Béchir Amri. The resulting formula expresses the Dunkl kernel in terms of the Dunkl kernel involving…
Sharp estimates for the Opdam-Cherednik -invariant heat kernel for the root system
Piotr Graczyk, Patrice Sawyer
For the first time, the estimates of the non-centered Weyl-group invariant heat kernel for curved Riemannian spaces and for Opdam-Cherednik Laplacians are studied systematically. W…
Sharp estimates for the hypergeometric functions related to root systems of type and of rank 1
Piotr Graczyk, Patrice Sawyer
In this article, we conjecture exact estimates for the Weyl-invariant Opdam-Cherednik hypergeometric functions. We prove the conjecture for the root system and for all rank 1…
Sharp estimates for -invariant Dunkl and heat kernels in the case
Piotr Graczyk, Patrice Sawyer
In this article, we prove exact estimates for the -invariant Dunkl kernel and heat kernel, for the root system of type with arbitrary positive multiplicities. We apply the e…
Sharp Estimates of Radial Dunkl and Heat Kernels in the Complex Case
P. Graczyk, P. Sawyer
In this article, we consider the radial Dunkl geometric case corresponding to flat Riemannian symmetric spaces in the complex case and we prove exact estimates for the positi…
Integral Kernels on Complex Symmetric Spaces and for the Dyson Brownian Motion
P. Graczyk, P. Sawyer
In this article, we consider flat and curved Riemannian symmetric spaces in the complex case and we study their basic integral kernels, in potential and spherical analysis: heat, N…
Potential kernels for radial Dunkl Laplacians
Piotr Graczyk, Tomasz Luks, Patrice Sawyer
We derive two-sided bounds for the Newton and Poisson kernels of the -invariant Dunkl Laplacian in geometric complex case when the multiplicity , i.e. for flat complex s…
Laplace-type representation for some generalized spherical functions of type BC
P. Sawyer
In [M. Rösler and M. Voit. Integral Representation and Uniform Limits for Some Heckman-Opdam Hypergeometric Functions of type BC, Transactions of the American Mathematical Society,…
A Laplace-type representation of the generalized spherical functions associated to the root systems of type A
Patrice Sawyer
In this paper, we extend the iterative expression for the generalized spherical functions associated to the root systems of type previously obtained beyond regular elements. We…
Convolution of orbital measures on symmetric spaces of type and
Piotr Graczyk, Patrice Sawyer
We study the absolute continuity of the convolution of two orbital measures on the symmetric spaces ${\bf SO}_0(p,p)/{\bf SO}(p)\times{\bf…
On the product formula on non-compact Grassmannians
Piotr Graczyk, Patrice Sawyer
We study the absolute continuity of the convolution of two orbital measures on the symmetric space $SO_0(p,q)/SO(p)\timesSO(q)$, . We…