Abstract
A complete description is given for the sequences {λk} ∞k=0 such that, for an arbitrary real polynomial\(f(t) = \sum\nolimits_{k = 0}^n {a_k t^k } \), an arbitraryA ε (0,+∞), and a fixedC ε (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].
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1323–1331, October, 1993.
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Bakan, A.G., Golub, A.P. On sequences that do not increase the number of real roots of polynomials. Ukr Math J 45, 1481–1489 (1993). https://doi.org/10.1007/BF01571083
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DOI: https://doi.org/10.1007/BF01571083