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Harmonic analysis on pseudo-Riemannian symmetric spaces of the group SL(2,R). (English. Russian original) Zbl 0542.43006

Math. USSR, Sb. 46, 493-506 (1983); translation from Mat. Sb., Nov. Ser. 118(160), 490-503 (1982).
Let G be a real semisimple Lie group, \(\tau\) be an involution of G, \(G^{\tau}\) be the subgroup of fixed points of \(\tau\). A pseudo- Riemannian symmetric space is a space \(X=G/H\) where H is an open subgroup of \(G^{\tau}\). The author studies the Plancherel formula on such spaces X for \(G=SL(2,R)\). The main tool in the study is the decomposition with respect to eigenfunctions of the radial part of the Laplace operator.
Reviewer: S.I.Gel’fand

MSC:

43A85 Harmonic analysis on homogeneous spaces
22E30 Analysis on real and complex Lie groups
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