Geodesic
S. R. Nasyrov's Problem of Approximation by Simple Partial Fractions on an Interval
Matematičeskie zametki, Tome 115 (2024) no. 4, pp. 568-577

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In 2014, S. R. Nasyrov asked whether it is true that simple partial fractions (logarithmic derivatives of complex polynomials) with poles on the unit circle are dense in the complex space $L_2[-1,1]$. In 2019, M. A. Komarov answered this question in the negative. The present paper contains a simple solution of Nasyrov's problem different from Komarov's one. Results related to the following generalizing questions are obtained: (a) of the density of simple partial fractions with poles on the unit circle in weighted Lebesgue spaces on $[-1,1]$; (b) of the density in $L_2[-1,1]$ of simple partial fractions with poles on the boundary of a given domain for which $[-1,1]$ is an inner chord.
Keywords: approximation, simple partial fraction
Mots-clés : Lebesgue space, constraints on poles. 
P. A. Borodin; A. M. Ershov. S. R. Nasyrov's Problem of Approximation by Simple Partial Fractions on an Interval. Matematičeskie zametki, Tome 115 (2024) no. 4, pp. 568-577. http://geodesic.mathdoc.fr/item/MZM_2024_115_4_a6/
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