Strictly positive definite functions on spheres

Strictly positive definite functions on spheres
HTML articles powered by AMS MathViewer

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.

References

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