On one property of zeros of polynomials of the least $$$(\alpha; \beta)$$$-deviation from zero in weighted space $$$L_p$$$

O.V. Polyakov (Oles Honchar Dnipro National University)

Abstract


We prove the property of monotonity of zeros of polynomials of the least $$$(\alpha; \beta)$$$-deviation from zero in the space with integral metrics with weight.

Keywords


polynomial; integral metric; $$$(\alpha; \beta)$$$-norm

References


Suyetin P.K. Classical orthogonal polynomials, Moscow, Nauka, 1976; 328 p. (in Russian)

Akhiezer N.I. Lectures on Approximation Theory, Moscow, Nauka, 1978; 463 p. (in Russian)

Korneichuk N.P., Babenko V.F., Ligun A.A. Extremum properties of polynomials and splines, Naukova dumka, Kyiv, 1992. (in Russian)

Kroo A., Peherstorfer F. "On the zeros of polynomials of minimal $$$L_p$$$-norm", Proc. Amer. Math. Soc., 1987; 101(4): pp. 652-656.




DOI: https://dx.doi.org/10.15421/241810

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ISSN (Online): 2518-7996
ISSN (Print): 2312-9557