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On unicity of complex polynomial $ L\sb{1}$-approximation along curves

Author: A. Kroó
Journal: Proc. Amer. Math. Soc. 86 (1982), 427-432
MSC: Primary 41A52; Secondary 30E10
MathSciNet review: 671209
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Abstract: We study the unicity of best polynomial $ {L_1}$-approximation of complex continuous functions along curves $ \gamma $ in the complex plane. A sufficient condition on $ \gamma $ is given which implies unicity. In particular our result includes the known cases of circle and line segment.

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

  • [1] S. Ja. Havinson, On uniqueness of functions of best approximation in the metric of the space $ {L^1}$, Izv. Akad. Nauk SSSR Ser. Mat. 22 (1958), 243-370. (Russian) MR 0101443 (21:254)
  • [2] B. R. Kripke and T. J. Rivlin, Approximation in the metric of $ {L^1}(X,\mu )$, Trans. Amer. Math. Soc. 119 (1965), 101-122. MR 0180848 (31:5078)
  • [3] I. Singer, Best approximation in normed linear spaces by elements of linear subspaces, Springer-Verlag, Berlin and New York, 1970. MR 0270044 (42:4937)

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Article copyright: © Copyright 1982 American Mathematical Society

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