Hostname: page-component-7479d7b7d-qs9v7 Total loading time: 0 Render date: 2024-07-12T08:31:10.572Z Has data issue: false hasContentIssue false

Convolution operators with trigonometric spline kernels

Published online by Cambridge University Press:  20 January 2009

T. N. T. Goodman
Affiliation:
Department of Mathematical Sciences, The University, Dundee DD1 4HN, Scotland
S. L. Lee
Affiliation:
School of Mathematical Sciences, University of Sciences of Malaysia, Penang, Malaysia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Bernstein polynomials are algebraic polynomial approximation operators which possess shape preserving properties. These polynomial operators have been extended to spline approximation operators, the Bernstein-Schoenberg spline approximation operators, which are also shape preserving like the Bernstein polynomials [8].

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Butzer, P. L. and Nessel, R. J., Fourier Analysis and Approximation (Academic Press, 1971).CrossRefGoogle Scholar
2.Goodman, T. N. T. and Lee, S. L., B-splines on the circle and trigonometric B-splines, Proc. Conference on Approximation Theory and Spline Functions (Singh, S. P., Bury, J. W. H. and Watson, B., eds., St. Johns, Newfoundland, Reidel Pub. Co., 1983), 297325.Google Scholar
3.Goodman, T. N. T. and Lee, S. L., Convexity preserving convolution operators, Proc. Conference on Constructive Approximation, Edmonton (1986), to appear.Google Scholar
4.Korovkin, P. P., Linear Operators and Approximation Theory (Hindustan Press, 1960).Google Scholar
5.Mairhuber, J., Schoenberg, I. J. and Williamson, R., On variation diminishing transformations on the circle, Rend. Circ. Mat. Palermo (2) 8 (1959), 241270.CrossRefGoogle Scholar
6.Schoenberg, I. J., On polynomial splines on the circle I, Proc. Conference on Constructive Theory of Functions (Budapest, 1972), 403433.Google Scholar
7.Schoenberg, I. J., On variation diminishing approximation methods, On Numerical Approximation (Ed. Langer, R. E., University of Wisconsin Press, 1959), 249274.Google Scholar
8.Schoenberg, I. J., On spline functions, Inequalities (Ed. Shisha, O., Academic Press, 1967), 255290.Google Scholar
9.Schumaker, L. L., Spline functions: Basic theory (Wiley, New York, 1981).Google Scholar