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

• Date: 1993
• Main Authors: Bakan, A. G., Holub, A. P., Бакан, А. Г., Голуб, А. П.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5937
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 \...