This article is cited in 4 papers

Approximation by linear fractional transformations of simple partial fractions and their differences

M. A. Komarov

Vladimir State University, 87 Gor’kogo str., Vladimir, 600000 Russia

Abstract: We study applications of a property of simple partial fractions such that a difference $f-\rho$, where $\rho$ is a simple partial fraction of order at most $n$, under linear-fractional transformations becomes again a difference of certain function and certain simple partial fraction of order at most $n$ with quadratic weight. We prove a theorem of uniqueness of interpolating simple partial fraction, generalizing known results, and obtain estimates of best uniform approximation of certain functions on real semi-axis $\mathbb{R}^+$. For the first time, for continuous functions of rather common type we obtain estimates of best approximation by differences of simple partial fractions on $\mathbb{R}^+$, and for odd functions on all axis $\mathbb{R}$.

Keywords: simple partial fraction, linear-fractional transformation, interpolation, best approximation, semi-axis, estimate, quadratic weight, differences of simple partial fractions.

UDC: 517.538

Received: 25.11.2016

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:3, 23–33

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