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Spherical functions on symmetric cones

- Patrice Sawyer
- Mathematics
- 1997

In this note, we obtain a recursive formula for the spherical functions associated with the symmetric cone of a formally real Jordan algebra. We use this formula as an inspiration for a similar… Expand

On an upper bound for the heat kernel on ${ m SU}sp ast(2n)/{ m Sp}(n)$

- Patrice Sawyer
- Mathematics
- 1 September 1994

The heat equation on the spaces of positive definite matrices

- Patrice Sawyer
- Mathematics
- 1 June 1992

The main topic of this paper is the study of the fundamental solution of the heat equation for the symmetric spaces of positive definite matrices, Pos(n,R). Our first step is to develop a «False Abel… Expand

Absolute continuity of convolutions of orbital measures on Riemannian symmetric spaces

- P. Graczyk, Patrice Sawyer
- Mathematics
- 1 October 2010

We study the absolute continuity of the measures δeX1♮⋆⋯⋆δeXm♮ and of (δeX♮)⋆l on the Riemannian symmetric spaces X of noncompact type for nonzero elements Xj, X∈a. For m,l⩾r+1, where r is the rank… Expand

CONVOLUTION OF ORBITAL MEASURES ON SYMMETRIC SPACES OF TYPE AND

- Piotr Graczyk, Patrice Sawyer
- Mathematics
- 24 March 2014

We study the absolute continuity of the convolution ${\it\delta}_{e^{X}}^{\natural }\star {\it\delta}_{e^{Y}}^{\natural }$
of two orbital measures on the symmetric spaces… Expand

ESTIMATES FOR THE HEAT KERNEL ON SL(n R) SO(n)

- Patrice Sawyer
- Mathematics
- 1 April 1997

In (1), Jean-Philippe Anker conjectures an upper bound for the heat kernel of a symmetric space of noncompact type. We show in this paper that his prediction is verified for the space of positive… Expand

ON EXACT INFERENCE FOR CHANGE IN A POISSON SEQUENCE

- H. Boudjellaba, B. MacGibbon, Patrice Sawyer
- Mathematics
- 28 February 2001

Since Hinkley's original work on exact inference for a change in a sequence of random variables, many authors have proposed different methods based either on exact distributions or asymptotic… Expand

Computing the Iwasawa decomposition of the classical Lie groups of noncompact type using the QR decomposition

- Patrice Sawyer
- Mathematics
- 15 March 2016

Abstract In this article, we show how the QR decomposition can be used to compute the Iwasawa decomposition for all classical Lie groups of noncompact type. This approach can also be used for the… Expand

A P ] 7 O ct 2 01 9 POTENTIAL KERNELS FOR RADIAL DUNKL LAPLACIANS

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… Expand

An analogue to the Duistermaat–Kolk–Varadarajan estimate for the spherical functions associated with the root systems of type A

- Patrice Sawyer
- Mathematics
- 2016

Abstract In this paper, we consider the generalized spherical functions ϕ λ ${\phi_{\lambda}}$ associated to the root systems of type A in order to provide an estimate in the spectral parameter λ.… Expand