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Approximation and interpolation by complex splines on the torus

Published online by Cambridge University Press:  20 January 2009

T. N. T. Goodman ,
S. L. Lee  and
A. Sharma
T. N. T. Goodman
Affiliation:
Department of Mathematical and Computing Sciences, University of Dundee, Dundee DD1 4HN, Scotland
S. L. Lee
Affiliation:
School of Mathematical and Computer Sciences, Science University of Malaysia, Penang 11800, Malaysia and Department of Mathematics, National University of Singapore, 10 Kent Crescent, Singapore 0511
A. Sharma
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
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Let T2 = {(eix1, eix2):0 ≦ xj<2π, j=1,2} be a two dimensional torus and r, s, t and k be positive integers with k>r+s+t–2. Our main object is to study the approximation and interpolation properties of a class of smooth functions whose restrictions to each triangle of a three direction mesh lie in the linear span of or 0≦μ≦r–1, r+s–l≦μ+ν≦r+s+t–2, or 0≦ν≦s–1, r+s–1≦μ+ν≦r+s+t–2} Where (z1, z2) ∈ T2.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 2 , June 1989 , pp. 197 - 212
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

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