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Uniqueness of a simple partial fraction of best approximation

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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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References

  1. V. I. Danchenko and D. Ya. Danchenko, “Approximation by simple fractions” [in Russian], Mat. Zametki 70, No. 4, 553–559 (2001); English transl.: Math. Notes 70, No. 4, 502–507 (2001).

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  2. V. I. Danchenko and E. N. Kondakova, “Chebyshev’s alternance in the approximation of constants by simple partial fractions” [in Russian], Trudy Mat. Inst. Steklova 270, 86–96 (2010); English transl.: Proc. Steklov Inst. Math. 270, 80–90 (2010).

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  3. V. I. Danchenko and D. Ya. Danchenko, “On the uniqueness of a simple partial fraction of best approximation” In: International Conference on Differential Equations and Dynamical Systems (Suzdal’, 2010), pp. 71–72, Steklov Inst. Math., Moscow (2010).

  4. E. N. Kondakova, “Interpolation by simple partial fractions” [in Russian], Izv. Sarat. Univ. Ser. Mat. 9, No. 2, 30–37 (2009).

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  5. Ya. V. Novak, Approximation and Interpolation Properties of Simple Partial Fractions [in Ukrainian], Ph. D. Thesis, Kiev, (2009).

  6. D. K. Faddeev and I. S. Sominskij, Problems in Higher Algebra [in Russian], Lan’. St.-Petersburg (2001); English transl.: W. H. Freemann and Company, San Francisco etc.(1965).

    Google Scholar 

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Authors and Affiliations

  1. Vladimir State University, 87, ul. Gor’kogo, Vladimir, 600000, Russia

    M. A. Komarov

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  1. M. A. Komarov
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Correspondence to M. A. Komarov.

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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

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