Integral formula and upper estimate of I and J-Bessel functions on   Jordan algebras
  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. 
Ryosuke Nakahama
math.RT math.CA