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Characterisation of correctness of cardinal interpolation with shifted three-directional box splines

Published online by Cambridge University Press:  14 November 2011

Ding-Xuan Zhou  and
Kurt Jetter
Ding-Xuan Zhou
Affiliation:
Fachbereich Mathematik, Universität Duisburg, D-47048 Duisburg, Germany
Kurt Jetter*
Affiliation:
Fachbereich Mathematik, Universität Duisburg, D-47048 Duisburg, Germany
*
†Any correspondence concerning the paper should be addressed to Professor Jetter.
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Extract

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 (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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 5 , 1995 , pp. 931 - 937
Copyright
Copyright © Royal Society of Edinburgh 1995

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