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Box-splines orthogonal projections (1812.01700v2)
Published 4 Dec 2018 in math.CA
Abstract: Let $P$ be orthogonal projection on B-splines of degree $r-1$ with equally spaced knots. Sweldens and Piessens proved that $P(xr)-xr$ 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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