Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102735
Title: Turán type converse Markov inequalities in Lq on a generalized Erőd class of convex domains
Authors: Glazyrina, P. Y.
Révész, S. G.
Issue Date: 2017
Publisher: Academic Press Inc.
Citation: Glazyrina P. Y. Turán type converse Markov inequalities in Lq on a generalized Erőd class of convex domains / P. Y. Glazyrina, S. G. Révész. — DOI 10.1016/j.jat.2017.05.004 // Journal of Approximation Theory. — 2017. — Vol. 221. — P. 62-76.
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 disk D:={z∈C:|z|≤1} and the interval I:=[−1,1], under the normalization condition that the zeros of the polynomial p in question all lie in D or I, resp. Namely, in 1939 he proved that with n:=degp tending to infinity, the precise growth order of the minimal possible derivative norm is n for D and n for I. Already the same year J. Erőd considered the problem on other domains. In his most general formulation, he extended Turán's order n result on D to a certain general class of piecewise smooth convex domains. Finally, a decade ago the growth order of the minimal possible norm of the derivative was proved to be n for all compact convex domains. Turán himself gave comments about the above oscillation question in Lq norm on D. Nevertheless, till recently results were known only for D, I and so-called R-circular domains. Continuing our recent work, also here we investigate the Turán-Erőd problem on general classes of domains. © 2017 Elsevier Inc.
Keywords: BERNSTEIN–MARKOV INEQUALITIES
BLASCHKE ROLLING BALL THEOREMS
CAPACITY
CHEBYSHEV CONSTANT
CONVEX DOMAINS
ERŐD DOMAIN
GABRIEL LEMMA
LOGARITHMIC DERIVATIVE
OUTER ANGLE
TRANSFINITE DIAMETER
TURÁN'S LOWER ESTIMATE OF DERIVATIVE NORM
URI: http://hdl.handle.net/10995/102735
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85033386473
PURE ID: 2039454
ISSN: 219045
DOI: 10.1016/j.jat.2017.05.004
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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