Distributions vectorielles homogènes sur une algèbre de Jordan

Bruno Blind (1)

1 IECN - Institut Élie Cartan de Nancy

We study distributions on a Euclidean Jordan algebra V with values in a finite dimensional representation space for the identity component G of the structure group of V and homogeneous equivariance condition. We show that such distributions exist if and only if the representation is spherical, and that then the dimension of the space of these distributions is r+1 ( where r is the rank of V). We give also construction of these distributions and of those that are invariant under the semi-simple part of G.

Domaines: Analyse fonctionnelle [math.FA]; Analyse classique [math.CA]

Bruno Blind. Distributions vectorielles homogènes sur une algèbre de Jordan. Journal of Functional Analysis, 2004, 208 (2), pp.482 - 507. ⟨hal-00146076⟩