Journal of Lie Theory 27 (2017), No. 1, 237--250
Copyright Heldermann Verlag 2017
On Functions of Negative Type on the Olshanski Spherical Pair (SL(∞), SU(∞))
Marouane Rabaoui
Dept. of Mathematics and Statistics, King Faisal University, P.O. Box 400, Al Ahsa 31982, Kingdom of Saudi Arabia
mrabaoui@kfu.edu.sa
Using a generalized Bochner type representation for Olshanski spherical pairs, we prove the boundedness of every SU(∞)-biinvariant continuous function of negative type on the infinite dimensional special linear group SL(∞).
Keywords: Function of negative type, function of positive type, spherical function, generalized Bochner theorem.
MSC: 22E30; 43A35, 43A85, 43A90
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