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Zap. Nauchn. Sem. POMI, 2014, Volume 429, Pages 106–120 (Mi znsl6070)  

On some rational functions which are analogues of Chebyshev polynomials

S. I. Kalmykovabc

a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia
b Bolyai Institute, University of Szeged, Szeged, Aradi v. tere1, 6720, Hungary
c Far Eastern Federal University, Vladivostok, Russia

Abstract: In this paper, rational functions, which are analogues of Chebyshev polynomials of the second, third and fourth kind, are considered. These rational functions are extremal in Bernstein type inequalities with corresponding weights. Orthogonalization of mentioned functions also is presented.

Key words and phrases: rational functions, Berstein-type inequalities, Chebyshev polynomials.

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English version:
Journal of Mathematical Sciences (New York), 2015, 207:6, 874–884

UDC: 517.54
Received: 01.08.2014

Citation: S. I. Kalmykov, “On some rational functions which are analogues of Chebyshev polynomials”, Analytical theory of numbers and theory of functions. Part 29, Zap. Nauchn. Sem. POMI, 429, POMI, St. Petersburg, 2014, 106–120; J. Math. Sci. (N. Y.), 207:6 (2015), 874–884

Citation in format AMSBIB
\Bibitem{Kal14}
\by S.~I.~Kalmykov
\paper On some rational functions which are analogues of Chebyshev polynomials
\inbook Analytical theory of numbers and theory of functions. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 429
\pages 106--120
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6070}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 207
\issue 6
\pages 874--884
\crossref{https://doi.org/10.1007/s10958-015-2411-8}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84949626758}


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