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Integral representations in Hardy classes and best approximations in certain functional spaces

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Ukrainian Mathematical Journal Aims and scope

Abstract

For the case of a simply connected domain in the plane one proves necessary and sufficient conditions for the representation of functions of the Hardy class H1 by an integral with respect to the harmonic measure of its boundary values. A theorem is given, characterizing the rate of decrease of the best polynomial approximations of an entire function in Hardy classes by the order and the type of this function.

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Literature cited

  1. P. L. Duren, Theory of HP Spaces, Academic Press, New York (1970).

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  2. A. A. Dovgoshei, “On the approximation by polynomials of functions from Hardy classes in simply connected domains in the plane,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 1, 16–18 (1990).

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  3. A. V. Batyrev, “On the question of the best approximation of an analytic function by polynomials,” Dokl. Akad. Nauk SSSR,76, 173–175 (1951).

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

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  5. A. Giroux, “Approximation of entire functions over bounded domains,” J. Approx. Theory,28, No. 1, 45–53 (1980).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Academy of Sciences of the Ukrainian SSR, Donetsk

    A. A. Dovgoshei

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  1. A. A. Dovgoshei
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 342–347, March, 1991.

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Dovgoshei, A.A. Integral representations in Hardy classes and best approximations in certain functional spaces. Ukr Math J 43, 306–311 (1991). https://doi.org/10.1007/BF01670070

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  • DOI: https://doi.org/10.1007/BF01670070

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