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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a new condition for strictly positive definite functions on spheres
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by Michael Schreiner PDF
Proc. Amer. Math. Soc. 125 (1997), 531-539 Request permission

Abstract:

Recently, Xu and Cheney (1992) have proved that if all the Legendre coefficients of a zonal function defined on a sphere are positive then the function is strictly positive definite. It will be shown in this paper that, even if finitely many of the Legendre coefficients are zero, the strict positive definiteness can be assured. The results are based on approximation properties of singular integrals, and provide also a completely different proof of the results of Xu and Cheney.
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Additional Information
  • Michael Schreiner
  • Affiliation: University of Kaiserslautern, Laboratory of Technomathematics, Geomathematics Group, P.O. Box 30 49, 67653 Kaiserslautern, Germany
  • Email: schreiner@mathematik.uni-kl.de
  • Received by editor(s): August 29, 1995
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 531-539
  • MSC (1991): Primary 43A35, 43A90, 42A82, 41A05
  • DOI: https://doi.org/10.1090/S0002-9939-97-03634-4
  • MathSciNet review: 1353398