论文标题
在未分离的线性微分方程解的零序列上
On non-separated zero sequences of solutions of a linear differential equation
论文作者
论文摘要
令$（z_k）$为单位光盘$ \ mathbb {d} $中无限点的序列。我们正在寻找$ a（z）$ in $ \ mathbb {d} $中的函数$ a（z）$，它具有具有零位为$ z_k $的解决方案，并且生成的函数$ a（z）$具有“最小”的增长。 We focus on the case of non-separated sequences $(z_k)$ in terms of the pseudohyperbolic distance when the coefficient $a(z)$ is of zero order, but $\sup_{z\in \mathbb{D}} (1-|z|)^p |a(z)|=+\infty$ for any $p>0$.我们在功能方面建立了$ a（z）$的最大模式的新估计值，$ n_z（t）= \ sum_ {| z_k_k-z | \ le t} 1 $ and $ n_z（r）= \ int_0^r \ frac {（n_z（n_z（n_z（n_z t）-1）-1）-1）-1）-1）-1）^+}^is stranciations stranciations。主要结果依赖于新的插值定理。
Let $(z_k)$ be a sequence of distinct points in the unit disc $\mathbb{D}$ without limit points there. We are looking for a function $a(z)$ analytic in $\mathbb{D}$ and such that possesses a solution having zeros precisely at the points $z_k$, and the resulting function $a(z)$ has `minimal' growth. We focus on the case of non-separated sequences $(z_k)$ in terms of the pseudohyperbolic distance when the coefficient $a(z)$ is of zero order, but $\sup_{z\in \mathbb{D}} (1-|z|)^p |a(z)|=+\infty$ for any $p>0$. We established a new estimate for the maximum modulus of $a(z)$ in terms of the functions $n_z(t)=\sum_{|z_k-z|\le t} 1 $ and $N_z(r)=\int_0^r \frac{(n_z(t)-1)^+}{t}dt.$ The estimate is sharp in some sense. The main result relies on a new interpolation theorem.
