Approximation by Λ-Splines on the Circle
Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1085-1111

Voir la notice de l'article provenant de la source Cambridge University Press

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, ζ 2, ..., ζ k−1 where We shall denote by or the class of Λ-splines S(z) which satisfy the following conditions: (i) S(z) ∊ C n−1(U) (ii) S(z)|Av ∊ Π(Λ) where
Goodman, T. N. T.; Lee, S. L.; Sharma, A. Approximation by Λ-Splines on the Circle. Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1085-1111. doi: 10.4153/CJM-1985-059-9
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[1] 1. Ahlberg, J. H., Nilson, E. N. and Walsh, J. L., Properties of analytic splines, I: Complex polynomial splines, J. of Analysis and Appl. 33 (1971), 234–257. Google Scholar

[2] 2. de Boor, C and Fix, G. J., Spline approximation by quasi-interpolants, J. Approx. Theory 8 (1973), 19–45. Google Scholar

[3] 3. Han-Lin, Chen, Interpolation and approximation on the unit circle, I, Math. Comp. No. 5/80 ISBN 82-7151-035-5 Quasi interpolant splines on the unit circle, J. Approx. Theory 38 (1983), 312–318. Google Scholar

[4] 4. Goodman, T. N. T. and Lee, S. L., B-splines on the circle and trigonometric B-splines, Proc. Conference on Approx. Theory, St. John's (Newfoundland). To appear. Google Scholar | DOI

[5] 5. Hirschman, I. I. and Widder, D. V., Generalized Bernstein polynomials, Duke Math J. 76 (1949), 433–438. Google Scholar

[6] 6. Lorentz, G. G., Bernstein polynomials (University of Toronto Press, Toronto, 1953). Google Scholar

[7] 7. Marsden, M. J., An identity for spline functions with applications to variation diminishing spline approximation, J. Approx, theory 3 (1970), 7–49. Google Scholar

[8] 8. Micchelli, C. A. and Sharma, A., Spline functions on the circle: Cardinal L-sp lines revisited, Can. J. Math. 32 (1980), 1459–1473. Google Scholar

[9] 9. Schumaker, L., Spline functions I (John Wiley & Sons, New York, 1981). Google Scholar

[10] 10. Schoenberg, I.J., On trigonometric spline interpolation, J. Math. Mech. 13 (1964), 795–826. Google Scholar

[11] 11. Schoenberg, I.J., On polynomial spline functions on the circle (I and II), Proceedings of the Conference on Constructive Theory of Functions (Budapest, 1972), 403–433. Google Scholar

[12] 12. Schoenberg, I.J., On variation diminishing approximation methods. In On numerical approximation, 249–274 MRC Symposium (U. of Wisconsin Press, Madison, 1959). Google Scholar

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