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

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

M. A. Komarov

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

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
\Bibitem{Kom18} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000427749600004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044107251} 

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• http://mi.mathnet.ru/eng/ivm/y2018/i3/p29

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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
2. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49
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