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On Global Properties of Polynomials Guaranteed by Their Behavior on a Subset

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Abstract

In this paper, we establish the order of growth of different norms of polynomials as a function of their degree by the given estimates of their values on a subset of the closed interval under consideration.

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REFERENCES

  1. V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow, 1977.

    Google Scholar 

  2. E. P. Dolzhenko and E. A. Sevast'yanov, “Sign-sensitive approximations (the space of sign-sensitive weights, stiffness and freedom of systems),” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 332 (1993), no. 6, 14-17.

    Google Scholar 

  3. S. B. Stechkin and P. L. Ul'yanov, Subsequences of the Convergence of Series [in Russian], Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], vol. 86, Nauka, Moscow, 1965.

    Google Scholar 

  4. S. N. Bernstein, “On a class of interpolation formulas,” in: Collected Works [in Russian], vol. 2, Moscow, 1954, pp. 146-154.

    Google Scholar 

  5. I. I. Sharapudinov, “On the boundedness in C[?1, 1] of the Vallée-Poussin means for the discrete Fourier-Chebyshev sums,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 187 (1996), no. 1, 143-160.

    Google Scholar 

  6. H. Ehrlich and K. Zeller, “Numeriche Abschätzung von Polynomen,” Z. Angew. Math. Mech., 45 (1965), T20-T22.

    Google Scholar 

  7. H. Ehrlich, “Polynomen zwischen Gitter-Punkten,” Math. Z., 93 (1966), 144-153.

    Google Scholar 

  8. D. Coppersmith and T. J. Rivlin, “The growth of polynomials of equally-spaced points,” SIAM J. Math. Anal., 23 (1992), 970-983.

    Google Scholar 

  9. I. P. Natanson, A Constructive Theory of Functions [in Russian], Moscow-Leningrad, 1949.

  10. E. P. Dolzhenko and E. A. Sevast'yanov, “On the definition of Chebyshev snakes,” Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.] (1994), no. 3, 49-59.

  11. S. Karlin and W. Studden, Tchebycheff Systems: With Applications in Analysis and Statistics, Interscience, New York, 1966.

    Google Scholar 

  12. A. A. Privalov, The Theory of Interpolation of Functions [in Russian], vol. 1, Izd. Saratov Univ., Saratov, 1990.

    Google Scholar 

  13. S. V. Konyagin, “Estimates of the derivatives of polynomials,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 243 (1978), no. 5, 1116-1118.

    Google Scholar 

  14. A. F. Timan, The Theory of Approximation of Functions of a Real Variable [in Russian], Moscow, 1960.

  15. I. I. Sharapudinov, “Estimation of the norm of an algebraic polynomial by its values at nodes of a uniform grid,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 188 (1997), no. 12, 135-156.

    Google Scholar 

  16. I. I. Sharapudinov, Orthogonal Polynomials on Grids. Theory and Applications [in Russian], DGPU, Makhachkala, 1997.

    Google Scholar 

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Authors and Affiliations

  1. Dagestan State University, Makhachkala

    N. Sh. Zagirov

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  1. N. Sh. Zagirov
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Zagirov, N.S. On Global Properties of Polynomials Guaranteed by Their Behavior on a Subset. Mathematical Notes 72, 308–324 (2002). https://doi.org/10.1023/A:1020591102814

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