Dirichlet空间中的正交函数

Orthogonal Functions in the Dirichlet Space

主要考虑了Dirichlet空间中的正交函数.主要结论表明单位圆盘中的一个解析自映射是Dirichlet空间中的正交函数,当且仅当其所对应的计数函数是本质径向的;当且仅当其所对应的诱导测度是径向的.作为主要结论的一个应用,给出了单位圆盘上的单叶解析函数和闭单位圆盘上的解析函数是Dirichlet空间中正交函数的完全刻画.

This paper focuses on orthogonal functions in the Dirichlet space.The authors show that an analytic self-map of the unit disk is orthogonal in the Dirichlet space if and only if the corresponding counting function is essential radial,and if and only if the corresponding induced measure is radial.As an application,the authors completely characterize orthogonal functions analytic in a neighborhood of the closed unit disk or univalent in the unit disk.