Ukrainian Mathematical Journal

, Volume 53, Issue 1, pp 1–14 | Cite as

On Some Properties of Orthogonal Polynomials over an Area in Domains of the Complex Plane. II

  • F. G. Abdullaev


We investigate polynomials that are orthonormal with weight over the area of a domain with quasiconformal boundary. We obtain new exact estimates for the growth rate of these polynomials.


Growth Rate Complex Plane Orthogonal Polynomial Exact Estimate Quasiconformal Boundary 
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  1. 1.
    F. G. Abdullaev, “On some properties of orthogonal polynomials over an area in domains of the complex plane. I,” Ukr. Mat. Zh. 52, No. 12, 1587–1595 (2000).Google Scholar
  2. 2.
    P. K. Suetin, “Orthogonal polynomials over an area and Bieberbach polynomials,” Tr. Mat. Inst. Akad. Nauk SSSR 100, 1–92 (1971).Google Scholar
  3. 3.
    D. Gaier, Lectures on Approximation Theory in a Complex Domain [Russian translation], Mir, Moscow (1986).Google Scholar
  4. 4.
    Yu. M. Berezanskii, G. F. Us, and Z. G. Sheftel', Functional Analysis [in Russian], Vyshcha Shkola, Kiev (1990).Google Scholar
  5. 5.
    A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Elementary Functions [in Russian], Nauka, Moscow (1981).Google Scholar
  6. 6.
    J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Plane AMS, Providence, RI (1969).Google Scholar
  7. 7.
    W. K. Hayman and P. B. Kennedy, Subharmonic Functions [Russian translation], Mir, Moscow (1980).Google Scholar
  8. 8.
    S. Stoilov, Theory of Functions of Complex Variables [in Russian], Vol. 2, Izd. Inostr. Liter., Moscow (1962).Google Scholar
  9. 9.
    V. V. Andrievskii and H. P. Blatt, Zeros of Polynomials in the Complex Plane Katholische Universitat, Eichstatt (1997).Google Scholar
  10. 10.
    A. I. Markushevich, Theory of Analytic Functions. Further Construction of the Theory [in Russian], Nauka, Moscow (1968).Google Scholar
  11. 11.
    V. V. Andrievskii, V. I. Belyi, and V. K. Dzjadyk, Conformal Invariants in Constructive Theory of Functions of Complex Variables World Federation, Atlanta, GA (1995).Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • F. G. Abdullaev
    • 1
  1. 1.Mersin UniversityTurkey

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