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Transactions of the American Mathematical Society

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Estimates for best approximation to rational functions


Author: S. J. Poreda
Journal: Trans. Amer. Math. Soc. 159 (1971), 129-135
MSC: Primary 30A82
DOI: https://doi.org/10.1090/S0002-9947-1971-0291475-6
MathSciNet review: 0291475
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Abstract: Estimates for the deviation of certain rational functions and their polynomials of best uniform approximation on various sets are given. As a result, in some cases these deviation and polynomials are explicitly calculated. For example, the polynomials of best uniform approximation to the function $ (\alpha z + \beta )/(z - a)(1 - \bar az),\vert a\vert \ne 1$, on the unit circle are given.


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

  • [1] N. I. Ahiezer, Lectures on the theory of approximation, OGIZ, Moscow, 1947; English transl., Ungar, New York, 1956. MR 10, 33; MR 20 #1872. MR 0025598 (10:33b)
  • [2] S. Ja. Al'per, Asymptotic values of best approximation of analytic functions in a complex domain, Uspehi Mat. Nauk 14 (1959), no. 1 (85), 131-134. (Russian) MR 21 #3577. MR 0104826 (21:3577)
  • [3] S. J. Poreda, Best approximation to some rational functions, Thesis, University of Maryland, College Park, Md., 1970.
  • [4] T. J. Rivlin, Some explicit polynomial approximations in the complex domain, Bull. Amer. Math. Soc. 73 (1967), 467-469. MR 35 #3068. MR 0212193 (35:3068)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0291475-6
Keywords: Best uniform approximation, rational function, lemniscate
Article copyright: © Copyright 1971 American Mathematical Society

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