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Eigenfunctions of the Beltrami-Laplace operator on a hyperboloid of one sheet

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Abstract

The Beltrami-Laplace operator Δ on a one-sheeted hyperboloid is hyperbolic. There is taken the set of functions bounded outside some neighborhood of two isotropic lines, intersecting at infinity. A necessary and sufficient condition is derived that a function of this set be an eigenfunction of the operator Δ.

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Literature cited

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Authors and Affiliations

  1. Moscow State Correspondence Pedagogical Institute, USSR

    V. -B. K. Rogov

Authors
  1. V. -B. K. Rogov
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Translated from Matematicheskie Zametki, Vol. 7, No. 2, pp. 255–263, February, 1970.

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Rogov, V.B.K. Eigenfunctions of the Beltrami-Laplace operator on a hyperboloid of one sheet. Mathematical Notes of the Academy of Sciences of the USSR 7, 152–157 (1970). https://doi.org/10.1007/BF01093501

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  • DOI: https://doi.org/10.1007/BF01093501

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