Characterisation of Correctness of Cardinal Interpolation with Shifted Three-Directional Box Splines

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Author(s)

  • Ding-Xuan Zhou
  • Kurt Jetter

Detail(s)

Original languageEnglish
Pages (from-to)931-937
Journal / PublicationProceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume125
Issue number5
Publication statusPublished - 1995
Externally publishedYes

Abstract

Cardinal interpolation by integer translates of shifted three-directional box splines is studied. It is shown that, for arbitrary orders, k,l, m ∊ N of the directional vectors, this problem is correct if and only if the shift vector is taken from the hexagonal shift region Ω:={(x,y)∈R2:~x~>½, ~y~>½, ~x-y~>½(modulo translation with respect to the lattice Z2). This confirms a conjecture of S. D. Riemenschneider [9], and settles the problem studied in [5] for the special case k = l = m in full generality. The method of proof is from homotopy theory. © 1995, Royal Society of Edinburgh. All rights reserved.