Title

Fundamental sets of continuous functions on spheres

Abstract

Let Sm and S∞ denote the unit spheres in Rm+1 and ℓ2, respectively. We look for functions f in C[-1, 1] such that the family of functions x → f (〈x, v〉) is fundamental in the space C(Sm). Here v runs over Sm. There is a similar question for C(S∞), when this space is given the topology of uniform convergence on compact sets.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1007/BF02678466

Keywords

Approximation, Continuous functions, Fundamentally, Positive-definite, Spheres

Publication Date

1-1-1997

Journal Title

Constructive Approximation

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