For citation:
Lukashov А. L., Tyshkevich S. V. Extremal Rational Functions on Several Arcs of the Unit Circle with Zeros on these Arcs. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, vol. 9, iss. 1, pp. 8-13. DOI: 10.18500/1816-9791-2009-9-1-8-13
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
18.03.2009
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Language:
Russian
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UDC:
517.51
Extremal Rational Functions on Several Arcs of the Unit Circle with Zeros on these Arcs
Autors:
Lukashov А. L., Saratov State University
Tyshkevich Sergey Viktorovich, Saratov State University
Abstract:
The solution of anextrema lproblem aboutrational function with fixed denominator and leading coefficient of nominator which is deviatedleast 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.
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