Skip to main content

The fundamentality of translates of a continuous function on spheres

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].

This is a preview of subscription content, access via your institution.

References

  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. W. Rudin,Real and Complex Analysis, 3rd ed. (McGraw-Hill, 1987).

  3. I.J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942) 96–108.

    Google Scholar 

  4. E.M. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, Princeton, NJ, 1971).

    Google Scholar 

  5. G. Szegö,Orthogonal Polynomials, Amer. Math. Colloq. Publ., vol. 23 (Amer. Math. Soc., Providence, RI, 1959).

    Google Scholar 

  6. Y. Xu and E.W. Cheney, Strictly positive definite functions on spheres, Proc. Amer. Math. Soc. 116 (1992) 977–981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by P.J. Laurent

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sun, X. The fundamentality of translates of a continuous function on spheres. Numer Algor 8, 131–134 (1994). https://doi.org/10.1007/BF02145700

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02145700

Keywords

  • Continuous Function
  • Euclidean Space
  • Unit Sphere