Mathematical Sciences: Krein Space Operators and Topics in Analysis

本课题旨在构建一个收缩理论 Krein空间上的算子，在诸如膨胀和 扩展属性，类似于希尔伯特空间的情况。 最近 工作表明，存在膨胀和延伸， 表征了 将研究新的标签问题。 示例包括由规范化的 单位圆盘子区域的黎曼映射。 一枚远程 目的是将该理论应用于系数插值问题 Riemann mappings映射 这个项目是在现代分析的一般领域， 涉及到空间和变换或算子的研究 在这些空间。 可能是最有研究价值的 物理学、分析学和几何学中的希尔伯特空间是希尔伯特空间。 Krein空间是一个标量空间， 可分解为a的正交直和的乘积 希尔伯特空间和希尔伯特空间的反空间。

This project is aimed at constructing a theory of contraction operators on Krein spaces which, in areas such as dilation and extension properties, parallels the Hilbert space case. Recent work has shown that dilations and extensions exist and can be characterized. New problems of labeling will be investigated. Examples include substitution operators induced by normalized Riemann mappings for subregions of the unit disk. A long-range goal is to apply the theory to a coefficient interpolation problem for Riemann mappings. This project is in the general area of modern analysis and involves the study of spaces and the transformations or operators on these spaces. Probably one of the most studied and valuable spaces in physics, analysis, and geometry is the Hilbert space. The Krein space examined in this project is a space with a scalar product which is decomposable as the orthogonal direct sum of a Hilbert space and the anti-space of a Hilbert space.