多项式的正交性与其零点有界性的一个注记

A Note on the Boundness of Zeros and Orthogonality

设{Φn(z)}n"=0是首一复正交多项式序列,其中Φn的次数为n,n≥1,且Φn的零点zn,j,j=1,2,…,n,满足|zn,j|<1.本文讨论{Φn(z)}n"=0的正交性,某个比值的有界性和条件|zn,j|<1,j=1,2,…,n之间的联系.

Let {φn（z） }n∞0 be a series of monic complex polynomials with deg φn = n , such that zn,j ,j = 1,2,--. ,n ,the zeros ofφn ,for each n ≥1, satisfy ｜z,,j ｜ 〈 1 . We es- tablish the relationship between the orthogonality of such a series, the boundness of a cer- tain ratio and the condition ｜ znj ｜ 〈 1 ,j = 1,2,..-,n.