C. Berg, J. P. Christensen, and P. , Harmonic analysis on semigroups .Theory of positive definite and related functions, 1984.

C. Berg and G. Forst, Potentiel theory on locally compact abelian groups, 1975.
DOI : 10.1007/978-3-642-66128-0

P. Billingsley, Convergence of probability measures, 1968.
DOI : 10.1002/9780470316962

A. Borodin and G. Olshanski, Infinite Random Matrices and Ergodic Measures, Communications in Mathematical Physics, vol.223, issue.1, pp.87-123, 2001.
DOI : 10.1007/s002200100529

URL : http://arxiv.org/abs/math-ph/0010015

K. R. Parthasarathy, Probability measures on metric spaces, 1967.
DOI : 10.1090/chel/352

M. Bouali, Application des th??or??mes de Minlos et Poincar?? ?? l?????tude asymptotique d???une int??grale orbitale, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.16, issue.1, 2006.
DOI : 10.5802/afst.1138

G. Choquet, Lectures on analysis II : Representation theory, Benjamin, 1969.

P. Courrège, Générateur infinitésimal d'un semi-groupe de convolution sur R n , et formule de Lévy-Khinchine, Bull. Sci. Math, vol.88, pp.3-10, 1964.

H. B. Curry and I. J. Schoenberg, On P??lya frequency functions IV: The fundamental spline functions and their limits, Journal d'Analyse Math??matique, vol.42, issue.1, pp.71-107, 1996.
DOI : 10.1007/BF02788653

J. Faraut and A. Korányi, Analysis on Symmetric Cones, 1994.

J. Faraut, Infinite dimensional harmonic analysis and probability, in probability measures on groups : Proceedings of the CIMPA-TIFR School. Recents Directions and Trends, TIFR, Mumbaï, 2006.

J. Faraut and K. Harzallah, Distances hilbertiennes invariantes sur un espace homog??ne, Annales de l???institut Fourier, vol.24, issue.3, pp.171-217, 1974.
DOI : 10.5802/aif.525

D. Freedman and P. Diaconis, A dozen de Finetti-style result in search of a theory, Probbilités et Statistiques), pp.397-423, 1987.

H. Glöckner, Positive definite functions on infinite-dimensional convex cones, Memoirs of the Amer, Math. Soc, vol.789, 2003.

P. Graczyk and J. J. Loeb, Bochner and Schoenberg theorems on symmetric spaces in the complex case, Bulletin de la Société mathématique de France, vol.122, issue.4, pp.122-571, 1994.
DOI : 10.24033/bsmf.2247

G. G. Hamedani and V. Mandrekar, Lévy-Khinchine representation and Banach spaces of type and cotype, Studia. Math, vol.6680, issue.3, pp.299-306, 1979.

M. Hervé, Analyticity in infinite dimensional spaces, 1989.
DOI : 10.1515/9783110856941

I. I. Hirschman and D. V. Widder, The convolution transform, 1955.

M. G. Krein, Hermitian kernels on homogeneous spaces, II, 1949.

J. Mickelsson, Current algebras and groups, 1989.
DOI : 10.1007/978-1-4757-0295-8

G. Olshanski, Unitary representations of infinite dimensional pairs (G, K) and the formalism sf R.Howe, in Representation of Lie groups and related topics Advanced Studies in contemporary, Mathematics, vol.7, 1990.

G. Olshanski, A. L. Vershikr, R. A. Dobroshin, M. A. Minlos, and . Shubin, Ergodic unitarily invariant measures on the space of infinite Hermitian matrices, Contemporary Mathematical physics, Vershik) Amer. Math. soc. Translations, pp.175137-175, 1996.

K. R. Parthasarathy, Probability measures on metric spaces, 1967.
DOI : 10.1090/chel/352

R. R. Phelps, Lecture on Choquet's theorem, 1966.
DOI : 10.1007/b76887

I. J. Schoenberg, Metric spaces and completely monotone functions. Ann. of math, pp.811-841, 1938.
DOI : 10.2307/1968466

S. R. Varadhan, Limit theorems for sums of independent random variables with values in a Hilbert space, pp.213-238, 1962.

A. M. Vershik, Description of invariant measures for the action of some infinite-dimensional groups, Dokl.Akad.Naud SSSR Soviet Math. Dokl, vol.218, issue.15, pp.749-752, 1974.

D. Voiculescu, Représentation factorielles de type II 1 de U (?), J. Math. pures et appl, vol.55, pp.1-22, 1976.

Y. Yamasaki, Measures on infinite dimensional spaces, World Scientific, vol.5, 1985.
DOI : 10.1142/0162