The backward shift on spaces of analytic functions

在这个项目中，PI计划研究单位圆盘上各种解析函数空间上的后向移位算子的不变子空间的‘连续性’性质。1970年，Douglas，Shapiro和Shields证明了属于Hardy空间的这些不变子空间的函数对外盘具有特殊的延拓性质。在最近的调查中，这种“延续”的想法已被证明是无处不在的，因为它似乎以这样或那样的形式发生在哈代空间案件的许多其他环境中。这项提案计划深入了解这些延期的性质以及它们最初发生的原因。这个项目属于数学分析领域的大标题，除了它的美丽和优雅之外，它还建立了许多联系，并植根于与物理和工程有关的问题。事实上，工程师S·达林顿最近研究了解析函数的“连续”性质的概念，他将这些“连续”性质与电路设计的性质联系起来。

In this project, the PI plans to investigate the `continuation' properties of the invariant subspaces of the backward shift operator on various spaces of analytic functions on the unit disk. In 1970, Douglas, Shapiro, and Shields showed that functions belonging to these invariant subspaces of the Hardy space posses special continuation properties to the exterior disk. In more recent investigations, this idea of `continuation' has been shown to be ubiquitous in that it appears to take place, in one form or another, in many other settings belong the Hardy space case. This proposal plans to get at the heart of the nature of these continuations and why they occur in the first place. This project falls under the broad heading of the field of mathematical analysis which, besides its beauty and elegance, makes many connections and has its roots in problems connected with physics and engineering. In fact, the concept of `continuation' properties of analytic functions has been recently studied by the engineer S. Darlington who connected these `continuations' to properties of electrical circuit design.