An improvement theorem for Descartes systems
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- by Philip W. Smith
- Proc. Amer. Math. Soc. 70 (1978), 26-30
- DOI: https://doi.org/10.1090/S0002-9939-1978-0467118-7
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Abstract:
An improvement (or comparison) theorem is proved for certain linear combinations of functions from a Descartes system. This theorem can then be applied to prove a conjecture of Lorentz, as well as more general results.References
- Itshak Borosh, Charles K. Chui, and Philip W. Smith, Best uniform approximation from a collection of subspaces, Math. Z. 156 (1977), no. 1, 13–18. MR 470578, DOI 10.1007/BF01215125
- Samuel Karlin and William J. Studden, Tchebycheff systems: With applications in analysis and statistics, Pure and Applied Mathematics, Vol. XV, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1966. MR 0204922
- Samuel Karlin, Charles A. Micchelli, Allan Pinkus, and I. J. Schoenberg (eds.), Studies in spline functions and approximation theory, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0393934
- G. M. Phillips, Error estimates for best polynomial approximations, Approximation Theory (Proc. Sympos., Lancaster, 1969) Academic Press, London, 1970, pp. 1–6. MR 0277970 A. Pinkus, Private communication.
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 70 (1978), 26-30
- MSC: Primary 41A50
- DOI: https://doi.org/10.1090/S0002-9939-1978-0467118-7
- MathSciNet review: 0467118