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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 2, Pages 282–296
DOI: https://doi.org/10.17377/smzh.2016.57.205 (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
Full-text PDF (501 kB) Citations (2)
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DOI: https://doi.org/10.17377/smzh.2016.57.205
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).
Received: 24.03.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 2, Pages 218–229
DOI: https://doi.org/10.1134/S0037446616020051
Bibliographic databases:
Document Type: Article
UDC: 517.5+517.53
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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