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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2022 Volume 111, Issue 1, Pages 3–7 (Mi mzm13223)

This article is cited in 1 paper

Approximation by Simple Partial Fractions: Universal Sets of Poles

P. A. Borodin

Moscow Center for Fundamental and Applied Mathematics

Abstract: For unbounded subsets E of the complex plane, we obtain conditions that are necessary or sufficient so that, for any compact set K that does not divide the plane, the simple partial fractions with poles in $E\setminus K$ approximate any function continuous on K and holomorphic inside K with an arbitrary accuracy uniformly on K.

Keywords: approximation, simple partial fractions, limit directions.

UDC: 517.538.5

Received: 15.07.2021
Revised: 24.08.2021

DOI: 10.4213/mzm13223


 English version:
Mathematical Notes, 2022, 111:1, 3–6

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© Steklov Math. Inst. of RAS, 2025