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JOURNALS // Journal of Siberian Federal University. Mathematics & Physics // Archive

J. Sib. Fed. Univ. Math. Phys., 2024 Volume 17, Issue 1, Pages 18–26 (Mi jsfu1134)

Chebyshev polynomials with zeros outside the open arc segment

Natalia N. Rybakova

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: The problem of unitary polynomials of degree $n$ with real coefficients least deviating from zero on an arbitrary fixed arc of a circle with a zero set outside an open segment of the same arc is considered. The description of the extremal polynomials of the solution of this problem is given and their norm depending on the degree of the polynomial and the arc length is obtained.

Keywords: Chebyshev polynomials, polynomials least deviating from zero, zero set, polynomials with real coefficients.

UDC: 517.538.5

Received: 18.06.2023
Received in revised form: 04.09.2023
Accepted: 14.11.2023

Language: English



© Steklov Math. Inst. of RAS, 2024