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

MSC 2020


26C10; 46E30; 41A50

References


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


Suyetin P.K. Classical orthogonal polynomials, Nauka, 1976.

Akhiezer N.I. Lectures on Approximation Theory, Nauka, 1978.

Korneichuk N.P., Babenko V.F., Ligun A.A. Extremum properties of polynomials and splines, Naukova dumka, 1992.




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

  

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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