摘要
假设A(z)在单位圆内解析,研究方程f″+A(z)f=0(*)非平凡解的零点序列{a_n},它们具有Bergman空间零点序列的特征,也即满足∑_n(1- |a_n|~2)^(1+δ)<∞对每一个δ>0.首先寻找A(z)的条件使得方程(*)的解属于Bergman空间A^2,这时这些解的零点序列显然具有上述特征.其次对于任给的零点序列{a_n},不是Blaschke序列,假设是一个A^(-α)插值序列(同样满足∑_n(1-|a_n|~2)^(1+δ)<∞对每一个δ>0),我们将构造一个解析函数A(z),使得{a_n}是方程(*)的某个解的零点序列,并且估计A(z)的增长.
Let A（z） be analytic in the unit disc, we study the zero sequences {αn} of the non-trivial solutions of
f″＋A（z）f=0（＊）
having the properties of zero sequences for the Bergman spaces, that is, satisfying ∑n（1-｜αn｜^2）1＋δ〈∞ for every δ 〉 0. We first find conditions on A（z） such that the solutions of （＊） belong to the Bergman space A^2, and so the zero sequences obviously have the above characterizations. For any given zero sequence {αn}, not the Blaschke sequence, assuming to be an interpolation sequence for A^-α （which also satisfying ∑n（1-｜αn｜^2）1＋δ〈∞ for any 5 〉 0）, we will construct an analytic function A（z） such that {αn} is the zero sequence of a solution of （＊）, and estimate the growth of A（z）.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2009年第2期371-380,共10页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(10571044)
