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Fundamental sets of continuous functions on spheres

Constructive Approximation volume 13, pages 245–250 (1997)Cite this article

Abstract

LetS m andS ∞ denote the unit spheres inR m+1 ande 2, respectively. We look for functionsf inC[−1, 1] such that the family of functionsx →f(<s,v>) is fundamental in the spaceC(S m). Herev runs overS m. There is a similar question forC(S ∞), when this space is given the topology of uniform convergence on compact sets.

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Authors and Affiliations

  1. Department of Mathematics, Southwest Missouri State University, 65804, Springfield, MO, USA

    Xingping Sun

  2. Department of Mathematics, University of Texas-Austin and University of Leicester, 78712-1082, Austin, TX, USA

    E. W. Cheney

Authors
  1. Xingping Sun
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  2. E. W. Cheney
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Additional information

Communicated by Tim Goodman.

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Sun, X., Cheney, E.W. Fundamental sets of continuous functions on spheres. Constr. Approx 13, 245–250 (1997). https://doi.org/10.1007/BF02678466

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  • DOI: https://doi.org/10.1007/BF02678466

AMS classification

  • 41A30
  • 41A45
  • 41A63
  • 42A65
  • 42A82
  • 42C10
  • 42C30

Key words and phrases

  • Spheres
  • Continuous functions
  • Fundamentality
  • Approximation
  • Positive-definite