We obtain a sufficient condition on the number of points of a Chebyshev alternance for the uniqueness of a simple partial fraction of degree n of best uniform approximation of a real-valued function on a segment of the real axis. We discuss the case where this number is greater than n + 1 and some aspects concerning approximations of constants. Bibliography: 6 titles.
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Translated from Problems in Mathematical Analysis 56, April 2011, pp. 63–82.
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Komarov, M.A. Uniqueness of a simple partial fraction of best approximation. J Math Sci 175, 284–308 (2011). https://doi.org/10.1007/s10958-011-0348-0
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DOI: https://doi.org/10.1007/s10958-011-0348-0