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Approximation by Spherical Functions

✍ Scribed by Hermann König

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
548 KB
Volume
162
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Results on the degree of approximation of continuous or Lipschitz‐continuous functions f:S^n−1^ → ℝ on the sphere in ℝ^n^ by spherical functions of degree k are given in terms of k and n, strengthening results of Newman and Shapiro. An example of (restriction of) a norm shows the result to be the best possible in k and n. Further, results for smoother functions are discussed.

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