TY - JOUR

T1 - The wave equation, O(2, 2), and separation of variables on hyperboloids

AU - Kalnins, E. G.

AU - Miller, W.

PY - 1978

Y1 - 1978

N2 - We classify group-theoretically all separable coordinate systems for the eigenvalue equation of the Laplace-Beltrami operator on the hyperboloid [FORMULA OMITED], finding 71 orthogonal and 3 non-orthogonal systems. For a number of cases the explicit spectral resolutions are worked out. We show that our results have application to the problem of separation of variables for the wave equation and to harmonic analysis on the hyperboloid and the group manifold SL(2, R). In particular, most past studies of SL(2, R) have employed only 6 of the 74 coordinate systems in which the Casimir eigenvalue equation separates.

AB - We classify group-theoretically all separable coordinate systems for the eigenvalue equation of the Laplace-Beltrami operator on the hyperboloid [FORMULA OMITED], finding 71 orthogonal and 3 non-orthogonal systems. For a number of cases the explicit spectral resolutions are worked out. We show that our results have application to the problem of separation of variables for the wave equation and to harmonic analysis on the hyperboloid and the group manifold SL(2, R). In particular, most past studies of SL(2, R) have employed only 6 of the 74 coordinate systems in which the Casimir eigenvalue equation separates.

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U2 - 10.1017/S0308210500019752

DO - 10.1017/S0308210500019752

M3 - Article

AN - SCOPUS:84971117034

VL - 79

SP - 227

EP - 256

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 3-4

ER -