2017
DOI: 10.1016/j.jat.2017.05.004
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Turán type converse Markov inequalities in Lq on a generalized Erőd class of convex domains

Abstract: Abstract. P. Turán was the first to derive lower estimations on the uniform norm of the derivatives of polynomials p of uniform norm 1 on the interval I := [−1, 1] and the disk D := {z ∈ C : |z| ≤ 1}, under the normalization condition that the zeroes of the polynomial p in question all lie in I or D, resp. Namely, in 1939 he proved that with n := deg p tending to infinity, the precise growth order of the minimal possible derivative norm is √ n for I and n for D. Already the same year J. Erőd considered the pro… Show more

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Cited by 7 publications
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