论文标题
Cartwright类功能和Helson-Szegö型条件的零密度
Density of zeros of the Cartwright class functions and the Helson--Szegö type condition
论文作者
论文摘要
b。\，ya。\，Levin已证明，正弦类型函数的零集可以作为有限数量的分离集合的结合，这是指数riesz碱基理论的重要结果。在本文中，我们将Levin的结果扩展到更通用的整个功能$ f（z）$，带有零件的$ 0 <q \ leq \ leq \ im z \ leq q，$，使得$ | f（x）|^2 $满足Helson-Szegö条件。此外，我们证明，而不是最后一个条件，可以要求$ \ log | f（x）| $属于BMO类。
B.\,Ya.\,Levin has proved that zero set of a sine type function can be presented as a union of a finite number of separated sets, that is an important result in the theory of exponential Riesz bases. In the present paper we extend Levin's result to a more general class of entire functions $F(z)$ with zeros in a strip $0<q \leq \Im z \leq Q,$ such that $|F(x)|^2$ satisfies the Helson--Szegö condition. Moreover, we demonstrate that instead of the last condition one can require that $\log|F(x)|$ belongs to the BMO class.
