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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

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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