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Algebraic solution of a problem of e.i. zolotarev and n. i. akhiezer on polynomials with smallest deviation from zero

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References

  1. N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Moscow (1965).

  2. N. I. Akhiezer, “The Chebyshev approach to function theory,” in: Mathematics in the XIX Century, Moscow (1987), pp. 9–97.

  3. M. G. Krein, “On inverse problems in the theory of filters of λ-zones of stability,” Dokl. Akad. Nauk SSSR,93, No. 5, 767–770 (1953).

    MATH  MathSciNet  Google Scholar 

  4. N. I. Akhiezer, “On one indefinite equation of Chebyshev type in probems on construction of orthogonal systems”, Mat. Fizika i Funktsion. Analiz., No. 2, 3–14 (1971).

    Google Scholar 

  5. M. G. Krein, B. Ya. Levin, and A. A. Nudelman, “On a special representation of polynomials that are positive on a system of closed intervals,” Am. Math. Soc. Transl. Ser. 2,142 (1989).

  6. P. M. Yuditskii, “On the outer envelope of families of rational functions that do not exceed unity on the unit disk and have fixed poles and zeros,” Dokl. Akad. Nauk SSSR,307, No. 4, 815–818 (1989).

    Google Scholar 

  7. N. I. Akhiezer, The Classical Moments Problem [in Russian], Moscow (1961).

  8. E. A. Gorin, “The Bernshtein inequalities from the viewpoint of operator theory,” Vestn. Khar'k. Univ., No. 205, 77–105 (1980).

    MATH  MathSciNet  Google Scholar 

  9. A. A. Markov, Collected Works on the Theory of Continued Fractions and Functions with Least Deviation from Zero [in Russian], Moscow-Leningrad (1948).

  10. N. I. Akhiezer, Elements of the Theory of Elliptic Functions [in Russian], Moscow (1970).

  11. B. C. Carlson and J. Todd, “Zolotarev's first problem,” Aequat. Math.,26, 1–33 (1983).

    MathSciNet  Google Scholar 

  12. B. C. Carlson and J. Todd, “The degenerating behavior of elliptic functions,” SIAM J. Numer. Anal.,20, No. 6, 1120–1129 (1983).

    MathSciNet  Google Scholar 

  13. F. Peherstorfer, “On Tchebysheff polynomials on disjoint intervals,” Coll. Math. Soc.,1, Budapest (1985), pp. 737–751.

    Google Scholar 

  14. F. Peherstorfer, “Orthogonal polynomials in L1-approximation,” Journ. Approx. Theory,52, No. 3, 241–268 (1988).

    MATH  MathSciNet  Google Scholar 

  15. F. Peherstorfer, “On Bernstein—Szegö orthogonal polynomials on several intervals II: orthogonal polynomials with periodic recurrence coefficients,” to appear in Journ. Approx. Theory, pp. 59–88.

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Authors
  1. M. L. Sodin
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  2. P. M. Yuditskii
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Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 56, pp. 56–64, 1991.

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Sodin, M.L., Yuditskii, P.M. Algebraic solution of a problem of e.i. zolotarev and n. i. akhiezer on polynomials with smallest deviation from zero. J Math Sci 76, 2486–2492 (1995). https://doi.org/10.1007/BF02364906

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  • DOI: https://doi.org/10.1007/BF02364906

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