Geodesic
Eigenfunctions of the Beltrami--Laplace operator on homogeneous pseudo-Riemannian symmetric spaces of rank 1
Sbornik. Mathematics, Tome 75 (1993) no. 2, pp. 371-404

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The Beltrami–Laplace operator on a homogeneous pseudo-Riemannian symmetric space of rank 1 is ultrahyperbolic in general. The present article gives a description of the eigenfunctions of this operator in a space of generalized functions with a restriction on their growth at infinity. 
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     author = {V. K. Rogov},
     title = {Eigenfunctions of the {Beltrami--Laplace} operator on homogeneous {pseudo-Riemannian} symmetric spaces of rank 1},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_75_2_a4/}
}
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V. K. Rogov. Eigenfunctions of the Beltrami--Laplace operator on homogeneous pseudo-Riemannian symmetric spaces of rank 1. Sbornik. Mathematics, Tome 75 (1993) no. 2, pp. 371-404. http://geodesic.mathdoc.fr/item/SM_1993_75_2_a4/