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

Zbl

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 
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/JOLT_2007_17_4_a7/
@article{JOLT_2007_17_4_a7,
     author = {A. R. Sinton},
     title = {The {Spherical} {Transform} on {Projective} {Limits} of {Symmetric} {Spaces}},
     journal = {Journal of Lie Theory},
     pages = {869--898},
     year = {2007},
     volume = {17},
     number = {4},
     zbl = {1135.43005},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2007_17_4_a7/}
}
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