Molchanov, V. F. 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 Keywords:pseudo-Riemannian symmetric space; Plancherel formula; decomposition; eigenfunctions; radial part of the Laplace operator PDFBibTeX XMLCite \textit{V. F. Molchanov}, Math. USSR, Sb. 46, 493--506 (1983; Zbl 0542.43006); translation from Mat. Sb., Nov. Ser. 118(160), 490--503 (1982) Full Text: DOI