scholarly journals Bernstein-Type Estimates for the Derivatives of Trigonometric Polynomials

2021 ◽  
Vol 28 (3) ◽  
pp. 31-40
Author(s):  
V. I. Danchenko ◽  
D. G. Chkalova
Keyword(s):  
Trigonometric Polynomials ◽  
Bernstein Type ◽  
Derivatives Of

Bernstein-Type Inequalities with Bombieri Norm

1996 ◽  
Vol 39 (2) ◽  
pp. 151-163
Author(s):  
Franck Beaucoup ◽  
Catherine Souchon
Keyword(s):  
Binomial Coefficient ◽  
Bernstein Type ◽  
Univariate Polynomial ◽  
Polar Derivatives ◽  
Image Position ◽  
Bernstein Type Inequalities ◽  
Derivatives Of

AbstractIf is an univariate polynomial with degree n then Bombieri norm of P is defined bywhere denotes the binomial coefficient.In the present paper we give, under assumptions on the roots of P, optimal Bernsteintype inequalities for the ratio between Bombieri norm of P and that of its derivative P′.We also give such inequalities for the polar derivatives of P defined by

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