Journal of Lie Theory 24 (2014), No. 2, 421--438
Copyright Heldermann Verlag 2014
Integral Formula and Upper Estimate of I and J-Bessel Functions on Jordan Algebras
Ryosuke Nakahama
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914, Japan
nakahama@ms.u-tokyo.ac.jp
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.
Keywords: Euclidean Jordan algebras, Bessel functions, holomorphic discrete series representations, holomorphic semigroups.
MSC: 33C10, 33C67, 17C30, 22E45, 47D06
[ Fulltext-pdf (357 KB)] for subscribers only.