Journal of Lie Theory 18 (2008), No. 1, 017--032
Copyright Heldermann Verlag 2008
A Lévy-Khinchin Formula for the Space of Infinite Dimensional Hermitian Matrices
Mohamed Bouali
Institut Préparatoire aux Études d'Ingénieur, 2, Rue Jawaher Lel Nahru, 1089 Montfleury, Tunisia
bouali@math.jussieu.fr
We give a Lévy-Kinchin formula for continuous negative definite functions defined on the space of Hilbert-Schmidt and Hermitian matrices which are invariant under the action by conjugation of the infinite dimensional unitary group.
Keywords: Negative definite function, positive definite function, spherical function.
MSC: 43A35, 43A90, 60B05, 60B10
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