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Harmonic analysis on hyperboloids. (English) Zbl 0253.43013

##### MSC:
 43A85 Harmonic analysis on homogeneous spaces 22E43 Structure and representation of the Lorentz group
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##### References:
 [1] Gelfand, I.M; Graev, M.I; Vilenkin, N.Ja, () [2] Helgason, S, Lie groups and symmetric spaces, () · Zbl 0177.50601 [3] Molčanov, V.F, Harmonic analysis on a hyperboloid of one sheet, Soviet math. dokl., 7, 1553-1556, (1966) · Zbl 0176.44303 [4] Molčanov, V.F, Analogue of the Plancherel formula for hyperboloids, Soviet math. dokl., 9, 1382-1385, (1968) · Zbl 0176.44304 [5] Riesz, M, L’intégral de Riemann-Liouville et le problème de Cauchy, Acta math., 8, 1-223, (1949) · Zbl 0033.27601 [6] Shintani, T, On the decomposition of regular representation of the Lorentz group on a hyperboloid of one sheet, (), 1-5 · Zbl 0184.17403 [7] Strichartz, R, The stationary observer problem for □u = mu and related equations, J. differential equations, 9, 205-223, (1971) · Zbl 0216.12803 [8] Takahashi, R, Sur LES représentations unitaires des groupes de Lorentz généralisés, Bull. soc. math. France, 91, 289-433, (1963) · Zbl 0196.15501 [9] Vilenkin, N.Ja, Special functions and the theory of group representations, Amer. math. soc. transl., 22, (1968) [10] Limic, N; Niederle, J; Raczka, R, Discrete degenerate representations of noncompact rotation groups, J. math. phys., 7, 1861-1876, (1966) · Zbl 0163.22802 [11] Limic, N; Niederle, J; Raczka, R, Continuous degenerate representations of noncompact rotation groups, J. math. phys., 7, 2026-2035, (1966) · Zbl 0158.45805 [12] Limic, N; Niederle, J; Raczka, R, Eigenfunction expansions associated with the second-order invariant operator on hyperboloids and cones, J. math. phys., 8, 1079-1093, (1967) · Zbl 0173.30102
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