Orthogonal projectors onto spaces of periodic splines

2016/08/24 by Passenbrunner, Markus
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1608.06720

Abstract

The main result of this paper is a proof that for any integrable function f on the torus, any sequence of its orthogonal projections (\widetildeP_n f) onto periodic spline spaces with arbitrary knots \widetildeΔ_n and arbitrary polynomial degree converges to f almost everywhere with respect to the Lebesgue measure, provided the mesh diameter |\widetildeΔ_n| tends to zero. We also give a proof of the fact that the operators \widetildeP_n are bounded on L^∞ independently of the knots \widetildeΔ_n.

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