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Uniform Approximation by Polynomial Solutions of Elliptic Systems on Boundaries of Carathéodory Domains in \(\boldsymbol{\mathbb{R}}^{\mathbf{2}}\)

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Abstract

We study the problem on uniform approximation of functions on compact subsets of the complex plane by polynomial solutions of general second-order elliptic systems with constant coefficients. This problem is well-known for the systems corresponding to second order equations with constant complex coefficients and is rather poor studied in the general case. In particular case, when the compact set where the approximation is considered is the boundary of a Carathéodory domain in the plane, we establish some new sufficient approximability conditions. We also discuss new measure orthogonality conditions that appear in the problem under consideration.

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Funding

The work was performed within the framework of the project 22-11-00071 by the Russian Science Foundation, except the results presented in Section 4 that were obtained in the framework of the project no. 19-11-00058 by the Russian Science Foundation.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991, Moscow, Russia

    K. Fedorovskiy

  2. St. Petersburg State University, 199034, St. Petersburg, Russia

    K. Fedorovskiy

  3. Moscow Center For Fundamental and Applied Mathematics, Lomonosov Moscow State University, 119991, Moscow, Russia

    K. Fedorovskiy

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  1. K. Fedorovskiy
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Correspondence to K. Fedorovskiy.

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(Submitted by F. G. Avhadiev)

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Fedorovskiy, K. Uniform Approximation by Polynomial Solutions of Elliptic Systems on Boundaries of Carathéodory Domains in \(\boldsymbol{\mathbb{R}}^{\mathbf{2}}\). Lobachevskii J Math 44, 1299–1310 (2023). https://doi.org/10.1134/S199508022304008X

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  • DOI: https://doi.org/10.1134/S199508022304008X

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