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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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Strictly positive definite functions on spheres
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by Yuan Xu and E. W. Cheney PDF
Proc. Amer. Math. Soc. 116 (1992), 977-981 Request permission


A sufficient condition is given for the strict positive-definiteness of a real, continuous function on the $m$-dimensional sphere.
  • Richard Askey, Orthogonal polynomials and special functions, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1975. MR 0481145
  • E. W. Cheney and Yuan Xu, A set of research problems in approximation theory, Topics in polynomials of one and several variables and their applications, World Sci. Publ., River Edge, NJ, 1993, pp. 109–123. MR 1276955
  • W. A. Light and E. W. Cheney, Interpolation by periodic radial basis functions, J. Math. Anal. Appl. 168 (1992), no. 1, 111–130. MR 1169852, DOI 10.1016/0022-247X(92)90193-H
  • I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942), 96–108. MR 5922
  • Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 977-981
  • MSC: Primary 43A35
  • DOI:
  • MathSciNet review: 1096214