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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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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
  2. [2]
    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
  4. [4]
    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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