Geodesic
Asymptotic Harmonic Analysis on the Space of Square Complex Matrices
Journal of Lie Theory, Tome 18 (2008) no. 3, pp. 645-670

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This paper is largely of expository nature. We determine the spherical functions of positive type on the space $V_\infty= M(\infty, {\bf C})$ relatively to the action of the product group $K_\infty = U(\infty)\times U(\infty)$. The space $V_\infty$ is the inductive limit of the spaces of square complex matrices $V_n=M(n, {\bf C})$, and the group $K_\infty$ is the inductive limit of the product groups $K_n=U(n) \times U(n)$, where $U(n)$ is the unitary group.
Classification : 22E30, 43A35, 43A85, 43A90
Mots-clés : Square complex matrices, unitary group, inductive limit, function of positive type, spherical function, ergodic measure, generalized Bochner theorem 
M. Rabaoui. Asymptotic Harmonic Analysis on the Space of Square Complex Matrices. Journal of Lie Theory, Tome 18 (2008) no. 3, pp. 645-670. http://geodesic.mathdoc.fr/item/JOLT_2008_18_3_a10/
@article{JOLT_2008_18_3_a10,
     author = {M. Rabaoui},
     title = {Asymptotic {Harmonic} {Analysis} on the {Space} of {Square} {Complex} {Matrices}},
     journal = {Journal of Lie Theory},
     pages = {645--670},
     year = {2008},
     volume = {18},
     number = {3},
     zbl = {1167.22008},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2008_18_3_a10/}
}
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