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arXiv · 1812.01700

Box-splines orthogonal projections

M. Beśka·K. Dziedziul
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Abstract

Let $P$ be orthogonal projection on B-splines of degree $r-1$ with equally spaced knots. Sweldens and Piessens proved that $P(x^r)-x^r$ is Bernoulli polynomial. We generalize Sweldens ans Piessens's result for box-splines. It gives the opportunity to define the seminorm of Sobolev space in terms of the asymptotic formula for the error in orthogonal projection.

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M. Beśka, K. Dziedziul. 2018-12-04. Box-splines orthogonal projections. https://arxiv.org/abs/1812.01700

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