This article is cited in 19 papers

Harmonic analysis on Riemannian symmetric spaces of negative curvature and scattering theory

M. A. Semenov-Tian-Shansky


Abstract: Harmonic analysis on a Riemannian symmetric space can be connected with the study of a nonstationary system of equations that has been constructed with respect to the ring of Laplace operators. The scattering theory for this system generalizes the scattering theory for hyperbolic equations constructed by Lax and Phillips. The paper contains a series of new spectral theorems generalizing the Harish–Chandra theorem and a formulation of a causality principle for scattering operators.
Bibliography: 23 titles.

UDC: 512.4+513.83

MSC: Primary 43A85; Secondary 35P25

Received: 23.12.1974

 English version: Mathematics of the USSR-Izvestiya, 1976, 10:3, 535–563

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