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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.Tere 1 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

Information

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

References

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