Abstract
Applying a quadrature rule with positive weights to some integral operators introduced by Newman and Shapiro we obtain generalized hyperinterpolation operators on the sphere, whose approximation error can be estimated — inspite of the discretisation — by means of the modulus of continuity. The main reason is that the weight distribution satisfies necessarily some regularity condition, which has been used before in hyperinterpolation by Sloan and Womersley, and which turned out to hold always by its own.
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Reimer, M. Discretized Newman-Shapiro Operators and Jackson’s Inequality on the Sphere. Results. Math. 36, 331–341 (1999). https://doi.org/10.1007/BF03322120
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DOI: https://doi.org/10.1007/BF03322120