On lie algebras of K-invariant functions
Toure, Ibrahima ; Kangni, Kinvi
J. Math. Kyoto Univ., Tome 48 (2008) no. 4, p. 847-855 / Harvested from Project Euclid
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Let $G$ be a locally compact group and let $K$ be a compact subgroup of $Aut(G)$, the group of automorphisms of $G$. $(G,K)$ is a Gelfand pair if the algebra $L_{K}^{1}(G)$ of K-invariant integrable functions on $G$ is commutative under convolution. In this paper, we give some charactezations of this algebra in the nilpotent case, which generalize some results obtained by C. Benson, J. Jenkins, G. Ratcliff in [1] and obtain a new criterion for Gelfand pairs.
Publié le : 2008-05-15
Classification:  430A20,  17B30 
@article{1250271320,
     author = {Toure, Ibrahima and Kangni, Kinvi},
     title = {On lie algebras of K-invariant functions},
     journal = {J. Math. Kyoto Univ.},
     volume = {48},
     number = {4},
     year = {2008},
     pages = { 847-855},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250271320}
}

Toure, Ibrahima; Kangni, Kinvi. On lie algebras of K-invariant functions. J. Math. Kyoto Univ., Tome 48 (2008) no. 4, pp.  847-855. http://gdmltest.u-ga.fr/item/1250271320/