Geodesic
The Spherical Transform on Projective Limits of Symmetric Spaces
Journal of Lie theory, Tome 17 (2007) no. 4, pp. 869-898.

Voir la notice de l'article provenant de la source Heldermann Verlag

The theory of a spherical Fourier transform for measures on certain projective limits of symmetric spaces of non-compact type is developed. Such spaces are introduced for the first time and basic properties of the spherical transform, including a Levy-Cramer type continuity theorem, are obtained. The results are applied to obtain a heat kernel measure on the limit space which is shown to satisfy a certain cylindrical heat equation. The projective systems under consideration arise from direct systems of semi-simple Lie groups {Gj} such that Gj is essentially the semi-simple component of a parabolic subgroup of Gj+1. This class includes most of the classical families of Lie groups as well as infinite direct products of semi-simple groups.
Classification : 43A85, 43A30
Mots-clés : Heat kernel, heat equation, projective limit, inverse limit, symmetric spaces, spherical Fourier transform, Lie group 
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     author = {A. R. Sinton },
     title = {The {Spherical} {Transform} on {Projective} {Limits} of {Symmetric} {Spaces}},
     journal = {Journal of Lie theory},
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     url = {http://geodesic.mathdoc.fr/item/JLT_2007_17_4_JLT_2007_17_4_a7/}
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A. R. Sinton . The Spherical Transform on Projective Limits of Symmetric Spaces. Journal of Lie theory, Tome 17 (2007) no. 4, pp. 869-898. http://geodesic.mathdoc.fr/item/JLT_2007_17_4_JLT_2007_17_4_a7/