Jackson-type inequality on the sphere

Author: Ditzian Zeev  

Publisher: Springer Publishing Company

ISSN: 0236-5294

Source: Acta Mathematica Hungarica, Vol.102, Iss.1-2, 2004-01, pp. : 1-36

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Abstract

In a recent paper, I introduced new moduli of smoothness for functions on the sphere which did not use averages and, as a result, had some interesting properties. The direct, Jackson-type, estimate of the best approximation by spherical harmonics using the new moduli will be proved here. Equivalence with the appropriate K-functionals will be given. Relations with the moduli used earlier will be shown and used to prove new results for these moduli.