Optimal uniform approximation on angles by entire functions |
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Authors: | S. Aleksanian N. Arakelian |
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Affiliation: | (1) Institute of Mathematics, NAS of Armenia, Yerevan, Armenia |
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Abstract: | The paper discusses the best or optimal uniform approximation problem by entire functions on a closed angle Δ. This problem has been studied by M.V. Keldysch in [4], under the assumption that the functions ? subject to approximation are holomorphic in a larger angle containing Δ and there is no restriction on the growth of ? at infinity. In [8], the problem was investigated for a wider class of functions ? continuously complex differentiable on Δ, with sharper estimates on the growth of approximating entire functions, linked with the growth of ? on Δ and the differential properties of ? on the boundary of Δ. In this paper, we improve some of the results on entire approximation on angles, using new approximation ideas partially presented in [9] and [10]. |
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Keywords: | Best uniform approximation Entire functions |
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