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Cardinal interpolation by symmetric exponential box splines on a three-direction mesh

Published online by Cambridge University Press:  20 January 2009

T. N. T. Goodman  and
A. A. Taani
T. N. T. Goodman
Affiliation:
Department of Mathematics and Computer Science, University of Dundee, Dundee, DD1 4HN, Scotland
A. A. Taani
Affiliation:
Department of Mathematics and Computer Science, University of Dundee, Dundee, DD1 4HN, Scotland
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Abstract

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We consider certain exponential box splines E on a three-direction mesh whose exponents satisfy a symmetry condition. It is shown, in particular, that given bounded data on the integer lattice in R2, there is a unique bounded combination of integer translates of E that interpolates the data. When all exponents are zero, this reduces to a result of de Boor, Höllig and Riemenschneider in [2]. Unlike the proof in [2] we use only elementary analysis and do not employ any computer calculations.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 2 , June 1990 , pp. 251 - 264
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

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