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Best $ L\sb 1$-approximation with varying weights


Author: András Kroó
Journal: Proc. Amer. Math. Soc. 99 (1987), 66-70
MSC: Primary 41A52; Secondary 41A65
DOI: https://doi.org/10.1090/S0002-9939-1987-0866431-4
MathSciNet review: 866431
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Abstract: It is proved in this note that the so-called $ A$-property is necessary in order that the finite-dimensional space $ U$ be Chebyshev in $ C\left( K \right)$ with respect to the norm $ \left\Vert f \right\Vert = \int_K {\omega \left\vert f \right\vert} $ for every positive continuous weight $ \omega $. It is also shown that for each finite-dimensional subspace $ U$ there exists a positive continuous weight $ \omega $ such that $ U$ is Chebyshev in $ C\left( K \right)$ with respect to this weight $ \omega $.


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

  • [1] A. Kroó, On an $ {L_1}$-Approximation problem, Proc. Amer. Math. Soc. 94 (1985), 406-410. MR 787882 (86h:41028)
  • [2] A. Pinkus, Unicity subspaces in $ {L^1}$-approximation, J. Approx. Theory (to appear).
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  • [4] -, Eindeutigkeit in der $ {L_1}$-Approximation, Math. Z. 176 (1981), 64-74.

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DOI: https://doi.org/10.1090/S0002-9939-1987-0866431-4
Article copyright: © Copyright 1987 American Mathematical Society

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