Invariant distributions on a non-isotropic pseudo-Riemannian symmetric   space of rank one
  We investigate the structure of invariant distributions on a non-isotropic non-Riemannian symmetric space of rank one. Especially, the $J$-criterion related to the generalized Gelfand pair is shown for this space without imposing the condition on the eigenfuction of the Laplace-Bertrami operator. 
Hiroyuki Ochiai