On a problem of integral geometry related to the Dirichlet problem for an ultrahyperbolic equation |
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Authors: | V. P. Burskii E. V. Kirichenko |
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Affiliation: | 1.Institute for Applied Mathematics and Mechanics,National Academy of Sciences,Donetsk,Ukraine |
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Abstract: | We study the nontrivial solvability of the homogeneous problem of integral geometry on the family of spheres formed by sections of the (n − 1)-dimensional unit sphere by hyperplanes perpendicular to the generators of a given cone. By using a relationship between this problem and the Dirichlet problem for an ultrahyperbolic equation in a ball and a criterion for the failure of uniqueness of the solution of the latter problem in terms of zeros of classical Jacobi polynomials, we obtain a criterion for the uniqueness of the solution of the former problem. |
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