Abstract:
We study a rate of uniform approximations on the real line of summable Lipschitz functions $f$ having a summable Hilbert transform $Hf$ by normalized logarithmic derivatives of rational functions. Inequalities between different metrics of the logarithmic derivatives of algebraic polynomials on the line are also considered.
Keywords:
logarithmic derivative of a rational function, simple partial fraction, Hilbert transform, uniform approximation, inequality between different metrics.
Citation:
M. A. Komarov, “Rational approximations of Lipschitz functions from the Hardy class on the line”, Probl. Anal. Issues Anal., 10(28):2 (2021), 54–66
\Bibitem{Kom21}
\by M.~A.~Komarov
\paper Rational approximations of Lipschitz functions from the Hardy class on the line
\jour Probl. Anal. Issues Anal.
\yr 2021
\vol 10(28)
\issue 2
\pages 54--66
\mathnet{http://mi.mathnet.ru/pa324}
\crossref{https://doi.org/10.15393/j3.art.2021.9530}
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\elib{https://elibrary.ru/item.asp?id=46863800}
Linking options:
https://www.mathnet.ru/eng/pa324
https://www.mathnet.ru/eng/pa/v28/i2/p54
This publication is cited in the following 1 articles:
P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851
Citation in format AMSBIB
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