Noncommutative Szego Theory, Moment Problems, and Related Problems in Noncommutative Analysis

非交换函数理论起源于J. L.泰勒在20世纪70年代，但最近经历了研究活动的激增。在2014年Kaliuzhnyi-Verbovetskyi和Vinnikov的一本广泛的专著的推动下，现在有一个丰富而活跃的理论可以被认为是“非交换复分析”。然而，到目前为止，大部分尚未开发的是Szego理论的相应的非对易模拟，或者更一般的单位圆上的正交多项式理论（OPUCs）。我们也将感兴趣的NC Szego理论的职能的Clifford代数变量。

Noncommutative (nc) function theory finds its origins in papers of J. L. Taylor in the 1970s, but much more recently has experienced a surge of research activity. Spurred in part by an extensive monograph by Kaliuzhnyi-Verbovetskyi and Vinnikov in 2014, there is now a rich and active theory of what can be thought of as "noncommutative complex analysis". As yet mostly untapped, however, is a corresponding noncommutative analogue of Szego theory, or more generally of the theory of Orthogonal Polynomials on the Unit Circle (OPUCs). We will also be interested in NC Szego theory for functions of a Clifford algebra variable.