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Orthogonal systems of functions associated with the solutions of Löwner's equation

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Abstract

This paper is devoted to LSwner's well-known method in the theory of univalent functions. Let

0<=t<∞, be the solution of Löwner's equation

under the initial condition

, and let

. Assume that the coefficients

are defined by the expansion

One proves the theorem: the functions

form an orthogonal system of functions on [0, ∞). One gives several corollaries of this theorem.

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Literature cited

  1. K. Löwner, “Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I,” Math. Ann.,89, 103–121 (1923).

    Google Scholar 

  2. G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Amer. Math. Soc., Providence (1969).

  3. I. E. Bazilevich (J. Basilewitsch),“Zum Koeffizientenproblem der schlichten Funktionen,” Mat. Sb.,1, No. 2, 211–228 (1936).

    Google Scholar 

  4. I. A. Aleksandrov, Parametric Continuations in the Theory of Univalent Functions [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  5. N. A. Lebedev, The Area Principle in the Theory of Univalent Functions [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  6. I. M. Milin, Univalent Functions and Orthonormal Systems, Amer. Math. Soc., Providence (1977).

  7. V. Ya. Gutlyanskii, “Parametric representations and extremal problems in the theory of univalent functions,” Author's Abstract of Doctoral Dissertation, Kiev (1972).

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Authors
  1. I. E. Bazilevich
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 24–35, 1983.

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Bazilevich, I.E. Orthogonal systems of functions associated with the solutions of Löwner's equation. J Math Sci 26, 2313–2322 (1984). https://doi.org/10.1007/BF01680010

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  • DOI: https://doi.org/10.1007/BF01680010

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