Abstract
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.
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REFERENCES
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).
P. K. Suetin, “Orthogonal polynomials over an area and Bieberbach polynomials,” Tr. Mat. Inst. Akad. Nauk SSSR 100, 1–92 (1971).
D. Gaier, Lectures on Approximation Theory in a Complex Domain [Russian translation], Mir, Moscow (1986).
Yu. M. Berezanskii, G. F. Us, and Z. G. Sheftel', Functional Analysis [in Russian], Vyshcha Shkola, Kiev (1990).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Elementary Functions [in Russian], Nauka, Moscow (1981).
J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Plane AMS, Providence, RI (1969).
W. K. Hayman and P. B. Kennedy, Subharmonic Functions [Russian translation], Mir, Moscow (1980).
S. Stoilov, Theory of Functions of Complex Variables [in Russian], Vol. 2, Izd. Inostr. Liter., Moscow (1962).
V. V. Andrievskii and H. P. Blatt, Zeros of Polynomials in the Complex Plane Katholische Universitat, Eichstatt (1997).
A. I. Markushevich, Theory of Analytic Functions. Further Construction of the Theory [in Russian], Nauka, Moscow (1968).
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).
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Abdullaev, F.G. On Some Properties of Orthogonal Polynomials over an Area in Domains of the Complex Plane. II. Ukrainian Mathematical Journal 53, 1–14 (2001). https://doi.org/10.1023/A:1010472331033
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DOI: https://doi.org/10.1023/A:1010472331033