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The V. A. Steklov problem in the theory of orthogonal polynomials

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Abstract

An exact order of growth of Szego polynomial kernels and moduli of polynomials orthogonal in the unit circle is obtained in the zeros of a weight function of special form. Other questions are also examined.

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Literature cited

  1. I. M. Glazman, Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators [in Russian], Moscow (1963).

  2. B. L. Golinskii, “On the growth of polynomial Szego kernels,” Teor. Funkts., Funkts. Analiz i ikh Prilozh., No. 10, 36–47 (1970).

    Google Scholar 

  3. Ya. L. Geronimus, Polynomials Orthogonal in a Circle and a Segment [in Russian], Moscow (1958).

  4. Ya. L. Geronimus, “Polynomials orthogonal in a circle and their application,” Zap. Khar'k. Matem. Ob-va,19, 35–120 (1948).

    Google Scholar 

  5. Ya. L. Geronimus, “On some limit properties of orthogonal polynomials,” Dokl. Akad. Nauk SSSR, No. 1, 19–20 (1965).

    Google Scholar 

  6. Ya. L. Geronimus, “On the dependence between the order of growth of orthonormal polynomials and the character of the imposition,” Matem. Sb., 61(103), No. 1, 65–79 (1963).

    Google Scholar 

  7. B. L. Golinskii, “On local limit relationships and asymptotic formulas for polynomials orthogonal in a unit circle,” Matem. Sb., 64(106), No. 3, 321–356 (1964).

    Google Scholar 

  8. G. Szego, Orthogonal Polynomials, American Mathematics Society (1967).

  9. T. Frey, “On the asymptotic behavior of orthogonal sequences of polynomials,” Matem. Sb.,49, 133–180 (1959).

    Google Scholar 

  10. P. K. Suetin, “Fundamental properties of polynomials orthogonal on a contour,” Uspekhi Matem. Nauk,51, No. 2(128), 41–48 (1966).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 15, No. 1, pp. 21–32, January, 1974.

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Golinskii, B.L. The V. A. Steklov problem in the theory of orthogonal polynomials. Mathematical Notes of the Academy of Sciences of the USSR 15, 13–19 (1974). https://doi.org/10.1007/BF01153538

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  • DOI: https://doi.org/10.1007/BF01153538

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