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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).
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
Linking options:
https://www.mathnet.ru/eng/smj2744 https://www.mathnet.ru/eng/smj/v57/i2/p282
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Abstract page: | 603 | Full-text PDF : | 98 | References: | 72 | First page: | 13 |
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