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.
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Ditzian, Z. Jackson-type inequality on the sphere. Acta Mathematica Hungarica 102, 1–36 (2004). https://doi.org/10.1023/B:AMHU.0000023207.17695.0d
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DOI: https://doi.org/10.1023/B:AMHU.0000023207.17695.0d