Email this article Sharp quadrature formulas and inequalities between various metrics for rational functions
- Authors: Danchenko V.I.1, Semin L.A.1
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Affiliations:
- Vladimir State University
- Issue: Vol 57, No 2 (2016)
- Pages: 218-229
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170356
- DOI: https://doi.org/10.1134/S0037446616020051
- ID: 170356
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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 L2-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).
About the authors
V. I. Danchenko
Vladimir State University
Author for correspondence.
Email: vdanch2012@yandex.ru
Russian Federation, Vladimir
L. A. Semin
Vladimir State University
Email: vdanch2012@yandex.ru
Russian Federation, Vladimir
