
Journal of Lie Theory 24 (2014), No. 2, 421438 Copyright Heldermann Verlag 2014 Integral Formula and Upper Estimate of I and JBessel Functions on Jordan Algebras Ryosuke Nakahama Graduate School of Mathematical Sciences, University of Tokyo, 381 Komaba Meguroku, Tokyo 1538914, Japan nakahama@ms.utokyo.ac.jp We give a new integral expression of I and JBessel 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 1dimensional semigroup 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 [ Fulltextpdf (357 KB)] for subscribers only. 