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One-Sided L1-Approximation

Published online by Cambridge University Press:  20 November 2018

A. Pinkus  and
V. Totik
A. Pinkus
Affiliation:
Department of Mathematics, Technion Haifa, Israel
V. Totik
Affiliation:
Bolyai Institute, Szeged Aradi V.Tere1 6720, Hungary
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Abstract

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Let Un be an n-dimensional subspace of C[0, 1]. We prove that if n ≥ 2, and Un contains a function which is strictly positive on (0, 1), then there exists an f ∈ C[0, 1] which has more than one best one-sided L '-approximation from Un. We also characterize those Un with the property that each f ∈ C[0, 1] has a unique best one-sided L1(w)-approximation from Un with respect to every strictly positive continuous weight function w.

Keywords

41A52
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 84 - 90
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. DeVore, R., One-sided approximation of functions, J. Approx. Theory 1 (1968), pp. 11—25.Google Scholar
2. Kroo, A., On an L1-approximation problem, Proc. Amer. Math. Soc. 94 (1985), pp. 406—410.Google Scholar
3. Pinkus, A., One-sided L1-approximation by splines with fixed knots, J. Approx. Theory 18 (1976), pp. 130–135.Google Scholar
4. Pinkus, A., Unicity subspaces in L1approximation, to appear in J. Approx. Theory.Google Scholar
5. Strauss, H., Unicity of best one-sided L1approximation, Numer. Math. 40 (1982), pp. 229—243.Google Scholar