Strictly positive definite functions on spheres

Authors:
Yuan Xu and E. W. Cheney

Journal:
Proc. Amer. Math. Soc. **116** (1992), 977-981

MSC:
Primary 43A35

MathSciNet review:
1096214

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Abstract | References | Similar Articles | Additional Information

Abstract: A sufficient condition is given for the strict positive-definiteness of a real, continuous function on the -dimensional sphere.

**[A]**Richard Askey,*Orthogonal polynomials and special functions*, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1975. MR**0481145****[CX]**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****[LC]**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**, 10.1016/0022-247X(92)90193-H**[S]**I. J. Schoenberg,*Positive definite functions on spheres*, Duke Math. J.**9**(1942), 96–108. MR**0005922****[Sz]**Gabor Szegö,*Orthogonal polynomials*, American Mathematical Society Colloquium Publications, Vol. 23. Revised ed, American Mathematical Society, Providence, R.I., 1959. MR**0106295**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1992-1096214-6

Article copyright:
© Copyright 1992
American Mathematical Society