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Cardinal interpolation with shifted three-directional box splines†

Published online by Cambridge University Press:  14 November 2011

Peter Binev  and
Kurt Jetter
Peter Binev
Affiliation:
Fachbereich Mathematik, Universität Duisburg, D-4100 Duisburg 1, Germany
Kurt Jetter
Affiliation:
Fachbereich Mathematik, Universität Duisburg, D-4100 Duisburg 1, Germany
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Synopsis

The question of “correctness” of cardinal interpolation with shifted three-directional box splines is solved for arbitrary orders of the directional vectors. It is shown that the corresponding symbol can be viewed as a collection of curves with certain properties (convexity, increasing argument, etc.) which are investigated in detail. The method of proof involves an induction argument which is based on properties of the exponential Euler splines (studied in [6]).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 122 , Issue 3-4 , 1992 , pp. 205 - 220
Copyright
Copyright © Royal Society of Edinburgh 1992

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References

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