On sequences that do not increase the number of real roots of polynomials - Bakan, A. G.; Holub, A. P. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
A complete description is given for the sequences {λ_k_k = 0^ ∞ such that, for an arbitrary real polynomial f(t) = olimits_k = 0^n a_k t^k , an arbitrary A (0, +∞), and a fixed C (0,+∞), the number of roots of the polynomial (Tf)(t) = olimits_k = 0^n a_k λ _k t^k on [0,C] does not exceed the number of roots off (t) on [0, A].