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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 3, Pages 29–40 (Mi ivm9336)  

This article is cited in 2 scientific papers (total in 2 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.

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

Bibliographic databases:

UDC: 517.538
Received: 25.11.2016

Citation: M. A. Komarov, “Approximation by linear fractional transformations of simple partial fractions and their differences”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 3, 29–40; Russian Math. (Iz. VUZ), 62:3 (2018), 23–33

Citation in format AMSBIB
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\by M.~A.~Komarov
\paper Approximation by linear fractional transformations of simple partial fractions and their differences
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 3
\pages 29--40
\mathnet{http://mi.mathnet.ru/ivm9336}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 3
\pages 23--33
\crossref{https://doi.org/10.3103/S1066369X18030040}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. A. Komarov, “O priblizhenii spetsialnymi raznostyami naiprosteishikh drobei”, Algebra i analiz, 30:4 (2018), 47–60  mathnet
    2. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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