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

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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.