Eigenfunctions of the Beltrami–Laplace operator on homogeneous pseudo-Riemannian symmetric spaces of rank 1

V.-B. K. Rogov


Abstract: 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.

UDC: 517.44+517.588

MSC: Primary 43A85, 35P10, 44A15; Secondary 53C35, 35J05, 58G30, 58G15

Received: 08.02.1991

 English version: Russian Academy of Sciences. Sbornik. Mathematics, 1993, 75:2, 371–404

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