The main result of the paper is a lower estimate for the moduli of imaginary parts of the poles of a simple partial fraction (i.e. the logarithmic derivative of an algebraic polynomial) under the condition that the \(L^\infty ({\mathbb {R}})\)-norm of the fraction is unit (Gorin’s problem). In contrast to the preceding results, the estimate takes into account the residues associated with the poles. Moreover, a new estimate for the moduli is obtained in the case when the \(L^\infty ({\mathbb {R}})\)-norm of the derivative of the simple partial fraction is unit (Gelfond’s problem).

中文翻译：

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单个简单部分分数的Gorin问题

本文的主要结果是，在\（L ^ \ infty（{\ mathbb {的情况下，），对简单部分分数（即代数多项式的对数导数）的极部的虚部的模量进行了较低的估计。R}}）\） -分数的范数是单位（Gorin问题）。与之前的结果相反，该估计考虑了与极点相关的残差。此外，当简单部分分数的导数的\（L ^ \ infty（{\ mathbb {R}}）\）范数为单位（Gelfond问题）时，可获得模量的新估计。