Geodesic
Integral Formula and Upper Estimate of I and J-Bessel Functions on Jordan Algebras
Ryosuke Nakahama1
1Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914, Japan
Journal of Lie Theory, Tome 24 (2014) no. 2, pp. 421-438

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 33C10, 33C67, 17C30, 22E45, 47D06
Mots-clés : Euclidean Jordan algebras, Bessel functions, holomorphic discrete series representations, holomorphic semigroups

Ryosuke Nakahama  1

1 Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914, Japan 
Ryosuke Nakahama. Integral Formula and Upper Estimate of I and J-Bessel Functions on Jordan Algebras. Journal of Lie Theory, Tome 24 (2014) no. 2, pp. 421-438. http://geodesic.mathdoc.fr/item/JOLT_2014_24_2_a5/
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     author = {Ryosuke Nakahama},
     title = {Integral {Formula} and {Upper} {Estimate} of {I} and {J-Bessel} {Functions} on {Jordan} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {421--438},
     year = {2014},
     volume = {24},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2014_24_2_a5/}
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