Numerical Algorithms

, Volume 8, Issue 1, pp 131–134 | Cite as

The fundamentality of translates of a continuous function on spheres

  • Xingping Sun
Article

Abstract

In this paper we discuss the fundamentality of translates of a continuous function on the unit spheres of Euclidean spaces. Our result partially answers a question of Cheney and Xu [1].

Keywords

Continuous Function Euclidean Space Unit Sphere 

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References

  1. [1]
    E.W. Cheney and Y. Xu, A set of research problems in approximation theory, in:Topics in Polynomials of One and Several Variables and Their Applications, eds. Th.M. Rassias, H.M. Srivastava and A. Yanushaukas (World Scientific, London, 1992).Google Scholar
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    W. Rudin,Real and Complex Analysis, 3rd ed. (McGraw-Hill, 1987).Google Scholar
  3. [3]
    I.J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942) 96–108.Google Scholar
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    E.M. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, Princeton, NJ, 1971).Google Scholar
  5. [5]
    G. Szegö,Orthogonal Polynomials, Amer. Math. Colloq. Publ., vol. 23 (Amer. Math. Soc., Providence, RI, 1959).Google Scholar
  6. [6]
    Y. Xu and E.W. Cheney, Strictly positive definite functions on spheres, Proc. Amer. Math. Soc. 116 (1992) 977–981.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1994

Authors and Affiliations

  • Xingping Sun
    • 1
  1. 1.Department of MathematicsSouthwest Missouri State UniversitySpringfieldUSA

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