Journal of Lie Theory

no. 2
Integral Formula and Upper Estimate of I and J-Bessel Functions on Jordan Algebras
Journal of Lie Theory, Volume 24 (2014) no. 2, pp. 421-438
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.
DOI: 10.5802/jolt.790
Classification: 33C10, 33C67, 17C30, 22E45, 47D06
Keywords: Euclidean Jordan algebras, Bessel functions, holomorphic discrete series representations, holomorphic semigroups 
@article{JOLT_2014_24_2_a5,
     author = {R. 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},
     doi = {10.5802/jolt.790},
     zbl = {1295.33007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.790/}
}
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R. Nakahama. Integral Formula and Upper Estimate of I and J-Bessel Functions on Jordan Algebras. Journal of Lie Theory, Volume 24 (2014) no. 2, pp. 421-438. doi: 10.5802/jolt.790

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