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- W2349958267 abstract "Let X be a list of vectors that is unimodular and let B X be the box spline defined by X. We discuss the proof of the following conjecture by Holtz and Ron: every real-valued function on the set of interior lattice points of the zonotope defined by X can be extended to a function on the whole zonotope of the form p(D)B X in a unique way, where p(D) is a differential operator that is contained in the so-called internal (mathcal{P})-space. We construct an explicit solution to this interpolation problem in terms of truncations of the Todd operator. As a corollary we obtain a slight generalisation of the Khovanskii-Pukhlikov formula that relates the volume and the number of lattice points in a smooth lattice polytope." @default.
- W2349958267 created "2016-06-24" @default.
- W2349958267 creator A5001523601 @default.
- W2349958267 date "2015-01-01" @default.
- W2349958267 modified "2023-09-24" @default.
- W2349958267 title "On a Conjecture of Holtz and Ron Concerning Interpolation, Box Splines, and Zonotopes" @default.
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- W2349958267 doi "https://doi.org/10.1007/978-3-319-20155-9_15" @default.
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