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Approximation of Non-Analytic Functions by Analytical Ones

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Abstract

We study the properties of the elements of best approximation for functions defined in the unit disk by functions from the Bergman space. For functions of a special type, we find a sufficiently accurate description of the properties of these elements in terms of the Hardy and Lipschitz classes. The obtained result is based on an analysis of the corresponding duality relation for extremal problems. The developed method is also applicable to relatively smooth (in terms of Sobolev spaces) approximated functions.

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Acknowledgments

Supported by Russian Foundation for Basic Research, grant No. 18-01-00017.

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Authors and Affiliations

  1. Chechen State University, bulv. Dudaeva 17a, Grozny, 364000, Russia

    H. H. Burchaev

  2. Don State Technical University, pl. Gagarina 1, Rostov-on-Don, 344000, Russia

    G. Yu. Ryabykh

Authors
  1. H. H. Burchaev
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  2. G. Yu. Ryabykh
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Corresponding authors

Correspondence to H. H. Burchaev or G. Yu. Ryabykh.

Additional information

Russian Text © H.H. Burchaev, G.Yu. Ryabykh, 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 1, pp. 18–28.

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Burchaev, H.H., Ryabykh, G.Y. Approximation of Non-Analytic Functions by Analytical Ones. Russ Math. 63, 14–23 (2019). https://doi.org/10.3103/S1066369X1901002X

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  • DOI: https://doi.org/10.3103/S1066369X1901002X

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