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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2009, Volume 9, Issue 1, Pages 8–13 (Mi isu27)  

Mathematics

Extremal rational functions on several arcs of the unit circle with zeros on these arcs

A. L. Lukashov, S. V. Tyshkevich

Saratov State University named after N. G. Chernyshevsky

Abstract: The solution of an extremal problem about rational function with fixed denominator and leading coefficient of nominator which is deviated least from zero on several arcs of the unit circle is given under restrictions on the location of zeros and additional conditions on mutual position of the arcs and zeros of denominator. The extremal function is represented in terms of the density of harmonic measure.

Key words: best approximation, extremal rational function, harmonic measure.

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UDC: 517.51

Citation: A. L. Lukashov, S. V. Tyshkevich, “Extremal rational functions on several arcs of the unit circle with zeros on these arcs”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 9:1 (2009), 8–13

Citation in format AMSBIB
\Bibitem{LukTys09}
\by A.~L.~Lukashov, S.~V.~Tyshkevich
\paper Extremal rational functions on several arcs of the unit circle with zeros on these arcs
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2009
\vol 9
\issue 1
\pages 8--13
\mathnet{http://mi.mathnet.ru/isu27}
\elib{http://elibrary.ru/item.asp?id=11903495}


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  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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