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Proceedings of the American Mathematical Society

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Simultaneous spline approximation and interpolation preserving norms

Authors: C. K. Chui, E. R. Rozema, P. W. Smith and J. D. Ward
Journal: Proc. Amer. Math. Soc. 54 (1976), 98-100
MathSciNet review: 0387917
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Abstract | References | Additional Information

Abstract: In this paper, it is proved that splines of order $ k(k \geqslant 2)$ have property SAIN. The proof of this result is based on the important properties of $ B$-splines.

References [Enhancements On Off] (What's this?)

  • [1] Carl de Boor, On calculating with 𝐵-splines, J. Approximation Theory 6 (1972), 50–62. Collection of articles dedicated to J. L. Walsh on his 75th birthday, V (Proc. Internat. Conf. Approximation Theory, Related Topics and their Applications, Univ. Maryland, College Park, Md., 1970). MR 0338617
  • [2] Frank Deutsch and Peter D. Morris, On simultaneous approximation and interpolation which preserves the norm, J. Approximation Theory 2 (1969), 355–373. MR 0252931
  • [3] Richard Holmes and Joseph Lambert, A geometrical approach to property (SAIN), J. Approximation Theory 7 (1973), 132–142. MR 0344769
  • [4] Joseph M. Lambert, Simultaneous approximation and interpolation in 𝐿₁ and 𝐶(𝑇), Pacific J. Math. 45 (1973), 293–296. MR 0318749
  • [5] -, Simultaneous approximation and interpolation which preserves the norm by cubic splines in $ C[a,b]$ (submitted).
  • [6] W. Wolibner, Sur un polynôme d’interpolation, Colloquium Math. 2 (1951), 136–137 (French). MR 0043946

Additional Information

Keywords: Property SAIN, spline approximation and interpolation, norm preservation, $ B$-spline
Article copyright: © Copyright 1976 American Mathematical Society

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