This article is cited in 3 papers

On the eigenfunctions of the Beltrami–Laplace operator on homogeneous symmetric spaces of rank 1

V.-B. K. Rogov


Abstract: This paper concerns itself with a differential equation which arises in the determination of the eigenfunctions of the Beltrami–Laplace operator on homogeneous symmetric spaces of rank 1. It is related to the Whittaker equation, and its coefficients are quadratic forms which do not depend on the variable of differentiation. All of the solutions of this equation in a space of generalized functions with restricted growth are described.
Bibliography: 7 titles.

UDC: 517.9

MSC: Primary 58G99; Secondary 46F05, 35R20

Received: 23.12.1975

 English version: Mathematics of the USSR-Sbornik, 1977, 33:2, 261–280

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