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Sibirsk. Mat. Zh., 2016, Volume 57, Number 2, Pages 282–296 (Mi smj2744)  

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

Sharp quadrature formulas and inequalities between various metrics for rational functions

V. I. Danchenkoa, L. A. Seminb

a Vladimir State University, Vladimir, Russia
b Vladimir State University, Vladimir, Russia

Abstract: We obtain the sharp quadrature formulas for integrals of complex rational functions over circles, segments of the real axis, and the real axis itself. Among them there are formulas for calculating the $L_2$-norms of rational functions. Using the quadrature formulas for rational functions, in particular, for simple partial fractions and polynomials, we derive some sharp inequalities between various metrics (Nikol'skiĭ-type inequalities).

Keywords: sharp quadrature formulas for rational functions, simple partial fraction, inequalities between various metrics (Nikol'skiĭ-type inequalities).

Funding Agency Grant Number
ДРПННиТ 1.1348.2011
Russian Foundation for Basic Research 14-01-00510
16-31-00252мол_а
Ministry of Education and Science of the Russian Federation 1.574.2016/ФПМ
The authors were supported by the DRPNNiT (Grant 1.1348.2011), the Russian Foundation for Basic Research (Grants 14-01-00510 and 16-31-00252 mol_a), the Ministry for Education and Science of the Russian Federation (Grants 2014/13 and 1.574.2016), and the Government Task for Vladimir State University (Grant 2014/13, Project 2868).


DOI: https://doi.org/10.17377/smzh.2016.57.205

Full text: PDF file (501 kB)
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English version:
Siberian Mathematical Journal, 2016, 57:2, 218–229

Bibliographic databases:

UDC: 517.5+517.53
Received: 24.03.2015

Citation: V. I. Danchenko, L. A. Semin, “Sharp quadrature formulas and inequalities between various metrics for rational functions”, Sibirsk. Mat. Zh., 57:2 (2016), 282–296; Siberian Math. J., 57:2 (2016), 218–229

Citation in format AMSBIB
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\by V.~I.~Danchenko, L.~A.~Semin
\paper Sharp quadrature formulas and inequalities between various metrics for rational functions
\jour Sibirsk. Mat. Zh.
\yr 2016
\vol 57
\issue 2
\pages 282--296
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\crossref{https://doi.org/10.17377/smzh.2016.57.205}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3510193}
\elib{http://elibrary.ru/item.asp?id=26237268}
\transl
\jour Siberian Math. J.
\yr 2016
\vol 57
\issue 2
\pages 218--229
\crossref{https://doi.org/10.1134/S0037446616020051}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84969670567}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
    2. P. Chunaev, V. Danchenko, “Quadrature formulas with variable nodes and Jackson-Nikolskii inequalities for rational functions”, J. Approx. Theory, 228 (2018), 1–20  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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