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


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; 304 p. (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://doi.org/10.15421/241810

  

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