论文标题
Dirichlet系列和紧凑型构图运算符的平均计数函数
A mean counting function for Dirichlet series and compact composition operators
论文作者
论文摘要
我们引入了DIRICHLET系列的平均计数函数，该功能在Dirichlet序列的Hardy空间函数理论中扮演着与Nevanlinna计数函数在经典理论中所做的相同的作用。平均计数函数的存在与Jessen和Tornehave对Lagrange平均运动问题的解决有关。我们使用平均计数函数来描述所有紧凑型构图操作员，并在Hardy-Hilbert Space系列中使用Dirichlet系列符号来描述Dirichlet系列的dirichlet系列符号，从而解决了一个问题，该问题自戈登（Gordon）和赫登马姆（Hedenmalm）描述了有限的组成运算符以来，该问题已经开发了。主要的结果是，当且仅当其符号的平均计数函数满足半平面边界处的衰减条件时，这种组成算子是紧凑的。
We introduce a mean counting function for Dirichlet series, which plays the same role in the function theory of Hardy spaces of Dirichlet series as the Nevanlinna counting function does in the classical theory. The existence of the mean counting function is related to Jessen and Tornehave's resolution of the Lagrange mean motion problem. We use the mean counting function to describe all compact composition operators with Dirichlet series symbols on the Hardy--Hilbert space of Dirichlet series, thus resolving a problem which has been open since the bounded composition operators were described by Gordon and Hedenmalm. The main result is that such a composition operator is compact if and only if the mean counting function of its symbol satisfies a decay condition at the boundary of a half-plane.
