The Australian Journal of Mathematical Analysis and Applications


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ISSN 1449-5910  

 

Paper Information

Paper Title:

Asymptotic Inequalities for the Maximum Modulus of the Derivative of a Polynomial

Author(s):

Clément Frappier


Département de Mathématiques et de Génie industriel École Polytechnique de Montréal,
C.P.~6079, succ. Centre-ville Montréal (Québec),
H3C 3A7, CANADA


clement.frappier@polymtl.ca.

 

Abstract:

Let be an algebraic polynomial of degree ≤n, and let ∥p∥= max {|p(z)|:|z| = 1}. We study the asymptotic behavior of the best possible constant φn,k (R), for k = 0 and k=1, in the inequality ∥p'(Rz)∥ + φn,k (R) |ak| ≤ nRn-1p∥, R → ∞.

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