2019
Том 71
№ 11

All Issues

On sequences that do not increase the number of real roots of polynomials

Bakan A. G., Holub A. P.

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Abstract

A complete description is given for the sequences $\{λ_k}_{k = 0}^{ ∞}$ such that, for an arbitrary real polynomial $f(t) = \sum\nolimits_{k = 0}^n {a_k t^k }$, an arbitrary $A \in (0, +∞)$, and a fixed $C \in (0,+∞)$, the number of roots of the polynomial $(Tf)(t) = \sum\nolimits_{k = 0}^n {a_k \lambda _k t^k }$ on $[0,C]$ does not exceed the number of roots off $(t)$ on $[0, A]$.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 10, pp 1481-1489.

Citation Example: Bakan A. G., Holub A. P. On sequences that do not increase the number of real roots of polynomials // Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1323–1331.

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