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≤u<v≤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.
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≤u<v≤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.
