论文标题
内部功能的关键结构
Critical structures of inner functions
论文作者
论文摘要
M. Heins的著名定理说，在Möbius转型后进行后组成，有限的Blaschke产品由其关键观点唯一决定。 K. Dyakonov建议将此结果扩展到无限程度可能很有趣，但是，由于内部功能可能具有相同的关键集合，因此需要谨慎。 在这项工作中，我们尝试通过加权伯格曼空间的1生成不变子空间来参数化内部函数$ a^2_1 $。我们的技术基于Liouville对应关系，该通信提供了复杂分析和非线性椭圆PDE之间的桥梁。
A celebrated theorem of M. Heins says that up to post-composition with a Möbius transformation, a finite Blaschke product is uniquely determined by its critical points. K. Dyakonov suggested that it may interesting to extend this result to infinite degree, however, one needs to be careful since inner functions may have identical critical sets. In this work, we try parametrizing inner functions by 1-generated invariant subspaces of the weighted Bergman space $A^2_1$. Our technique is based on the Liouville correspondence which provides a bridge between complex analysis and non-linear elliptic PDE.
