AN INEQUALITY FOR POLYNOMIALS WITH A PRESCRIBED ZERO

作     者：Dewan K.K. Govil N.K. 

作者机构：Jamia Millia Islamia India Auburn University. U.S.A. 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：1994年第10卷第3期

页      面：104-106页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Trigonometric Polynomial Prescribe Zero 

摘      要：Let p_n(z)=∑_(k-0)~n a_kz^k be a polynomial of degree n such that |p_n(z)|≤M for |z|≤1. It is well. known that for 0≤uv≤n, |a_u|+|a_|≤4M/π and this result is best possible. In this paper we sharpen the above inequlity for polynomials p_n(z) having a zero on |z|=1 or (more generally) if |p_n(1)|=a, 0≤a≤1.