An indefinite analog of Sarason's generalized interpolation theorem
Speaker:
James Rovnyak, University of Virginia
Date and Time:
Friday, October 8, 2021 - 11:00am to 11:50am
Location:
Online
Abstract:
Sarason's generalized interpolation theorem gives the form of an operator $R$ on a model space that commutes with the compression of the shift operator. This lecture will discuss an analogous result when $1-RR^*$ has a finite number of negative squares. An indefinite version of Nudel'man's problem is first used to show that $R$ satisfies an operator identity involving a finite Blaschke product. An independent study of root subspaces in ${\mathcal H}(B)$ spaces is then used to deduce the form of $R$ from the operator identity.