A modulus of smoothness on the unit sphere
For functions onS d−1 (the unit sphere inR d) and, in particular, forf∈L p(S d−1), we define new simple moduli of smoothness. We relate different orders of these moduli, and we also relate these moduli to best approximation by spherical harmonics of order smaller thann. Our new moduli lead to sharper results than those now available for the known moduli onL p(S d−1).
KeywordsBanach Space Unit Sphere Spherical Harmonic Triangle Inequality Orthogonal Matrix
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