Integral formula and upper estimate of I and J-Bessel functions on Jordan algebras

Abstract

In this paper we give a new integral expression of I and J-Bessel functions on simple Euclidean Jordan algebras, integrating on a bounded symmetric domain. From this we easily get the upper estimate of Bessel functions. As an application we give an upper estimate of the integral kernel function of the holomorphic 1-dimensional semi-group acting on the space of square integrable functions on symmetric cones.

18 pages

References in corpus (2)

• Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups
• A geometric quantization of the Kostant-Sekiguchi correpondence for scalar type unitary highest weight representations

Cited by in corpus (2)

• A geometric quantization of the Kostant-Sekiguchi correpondence for scalar type unitary highest weight representations
• Beta distributions and Sonine integrals for Bessel functions on symmetric cones