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Approximation by Λ-Splines on the Circle

Published online by Cambridge University Press:  20 November 2018

T. N. T. Goodman ,
S. L. Lee  and
A. Sharma
T. N. T. Goodman
Affiliation:
University of Dundee, Dundee, Scotland
S. L. Lee
Affiliation:
University of Dundee, Dundee, Scotland
A. Sharma
Affiliation:
University of Dundee, Dundee, Scotland
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Let Λ = {λ0,…, λn} denote a set of distinct integers and let Π(Λ) denote the set of all generalized polynomials of the form

For any given ζ on the unit circle U with

we consider the set Zk of points 1, ζ, ζ2, …, ζk−1 where

We shall denote by or the class of Λ-splines S(z) which satisfy the following conditions:

  • (i) S(z) ∊ Cn−1(U)

  • (ii) S(z)|Av ∊ Π(Λ) where

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 6 , 01 December 1985 , pp. 1085 - 1111
Copyright
Copyright © Canadian Mathematical Society 1985

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