Best -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 -property is necessary in order that the finite-dimensional space be Chebyshev in with respect to the norm for every positive continuous weight . It is also shown that for each finite-dimensional subspace there exists a positive continuous weight such that is Chebyshev in with respect to this weight .

**[1]**András Kroó,*On an 𝐿₁-approximation problem*, Proc. Amer. Math. Soc.**94**(1985), no. 3, 406–410. MR**787882**, https://doi.org/10.1090/S0002-9939-1985-0787882-0**[2]**A. Pinkus,*Unicity subspaces in**-approximation*, J. Approx. Theory (to appear).**[3]**Hans Strauss,*Uniqueness in 𝐿₁-approximation for continuous functions*, Approximation theory, III (Proc. Conf., Univ. Texas, Austin, Tex., 1980), Academic Press, New York-London, 1980, pp. 865–870. MR**602812****[4]**-,*Eindeutigkeit in der**-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