A Sharp Version of Mahler’s Inequality for Products of Polynomials
نویسندگان
چکیده
In this note we give some sharp estimates for norms of polynomials via the products of norms of their linear terms. Different convex norms on the unit disc are considered.
منابع مشابه
An Areal Analog of Mahler’s Measure
We consider a version of height on polynomial spaces defined by the integral over the normalized area measure on the unit disk. This natural analog of Mahler’s measure arises in connection with extremal problems for Bergman spaces. It inherits many nice properties such as the multiplicative one. However, this height is a lower bound for Mahler’s measure, and it can be substantially lower. We di...
متن کاملRemez-type Inequalities on the Size of Generalized Polynomials
Generalized polynomials are defined as products of polynomials raised to positive real powers. The generalized degree can be defined in a natural way. A number of classical inequalities holding for polynomials can be extended for generalized polynomials utilizing the generalized degree in place of the ordinary one. Remez established a sharp upper bound for the maximum modulus on [— 1,1] of alge...
متن کاملSharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs
In $1994,$ degree distance of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the multiplicative version of degree distance and multiplicative ver...
متن کاملPolynomial Inequalities, Mahler’s Measure, and Multipliers
We survey polynomial inequalities obtained via coefficient multipliers, for norms defined by the contour or the area integrals over the unit disk. Special attention is devoted to the Szegő composition and the inequalities related to Mahler’s measure. We also consider a new height on polynomial spaces defined by the integral over the normalized area measure on the unit disk. This natural analog ...
متن کاملProducts of Polynomials in Uniform Norms
We study inequalities connecting a product of uniform norms of polynomials with the norm of their product. This subject includes the well known Gel’fond-Mahler inequalities for the unit disk and Kneser inequality for the segment [−1, 1]. Using tools of complex analysis and potential theory, we prove a sharp inequality for norms of products of algebraic polynomials over an arbitrary compact set ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999