Abstract
The translation of a function f on the surface of the unit sphere in k — dimensional Euclidean space is defined by the integral means of f over the circle >x,y< = h on the sphere. Via this translation there are introduced the strong Laplace — Beltrami differential operator and the r — th modulus of continuity of functions defined on the sphere. The rate of best approximation by sums of spherical harmonics of degree ⩽ n is then completely characterized by higher order Lipschitz conditions and differentiability properties.
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Wehrens, M. (1981). Best Approximation on the Unit Sphere in \( {\mathbb{R}^k} \) . In: Butzer, P.L., Sz.-Nagy, B., Görlich, E. (eds) Functional Analysis and Approximation. ISNM 60: International Series of Numerical Mathematics / ISNM 60: Internationale Schriftenreihe zur Numerischen Mathematik / ISNM 60: Série internationale d’Analyse numérique, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9369-5_22
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