Quadrature formulas with variable nodes and Jackson–Nikolskii inequalities for rational functions

Petr Chunaev; Vladimir Danchenko

doi:10.1016/j.jat.2017.12.004

Quadrature formulas with variable nodes and Jackson–Nikolskii inequalities for rational functions

Petr Chunaev, Vladimir Danchenko

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

© 2018 Elsevier Inc. We obtain new parametric quadrature formulas with variable nodes for integrals of complex rational functions over circles, segments of the real axis and the real axis itself. Basing on these formulas we derive (q,p)-inequalities of Jackson–Nikolskii type for various classes of rational functions, complex polynomials and their logarithmic derivatives (simple partial fractions). It is shown that our (∞,2)- and (∞,4)-inequalities are sharp in a number of main theorems. Our inequalities extend and refine several results obtained earlier by other authors.

Original language	English
Pages (from-to)	1-20
Journal	Journal of Approximation Theory
Volume	228
DOIs	https://doi.org/10.1016/j.jat.2017.12.004
Publication status	Published - 1 Apr 2018

Keywords

Jackson–Nikolskii inequalities
Quadrature formulas
Rational functions

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10.1016/j.jat.2017.12.004

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abstract = "{\textcopyright} 2018 Elsevier Inc. We obtain new parametric quadrature formulas with variable nodes for integrals of complex rational functions over circles, segments of the real axis and the real axis itself. Basing on these formulas we derive (q,p)-inequalities of Jackson–Nikolskii type for various classes of rational functions, complex polynomials and their logarithmic derivatives (simple partial fractions). It is shown that our (∞,2)- and (∞,4)-inequalities are sharp in a number of main theorems. Our inequalities extend and refine several results obtained earlier by other authors.",

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AU - Chunaev, Petr

AU - Danchenko, Vladimir

PY - 2018/4/1

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N2 - © 2018 Elsevier Inc. We obtain new parametric quadrature formulas with variable nodes for integrals of complex rational functions over circles, segments of the real axis and the real axis itself. Basing on these formulas we derive (q,p)-inequalities of Jackson–Nikolskii type for various classes of rational functions, complex polynomials and their logarithmic derivatives (simple partial fractions). It is shown that our (∞,2)- and (∞,4)-inequalities are sharp in a number of main theorems. Our inequalities extend and refine several results obtained earlier by other authors.

AB - © 2018 Elsevier Inc. We obtain new parametric quadrature formulas with variable nodes for integrals of complex rational functions over circles, segments of the real axis and the real axis itself. Basing on these formulas we derive (q,p)-inequalities of Jackson–Nikolskii type for various classes of rational functions, complex polynomials and their logarithmic derivatives (simple partial fractions). It is shown that our (∞,2)- and (∞,4)-inequalities are sharp in a number of main theorems. Our inequalities extend and refine several results obtained earlier by other authors.

KW - Jackson–Nikolskii inequalities

KW - Quadrature formulas

KW - Rational functions

UR - https://www.scopus.com/pages/publications/85044854235

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DO - 10.1016/j.jat.2017.12.004

M3 - Article

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VL - 228

SP - 1

EP - 20

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

ER -

Quadrature formulas with variable nodes and Jackson–Nikolskii inequalities for rational functions

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Keywords

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