Alan Sola: Pairs of Clark operators and their Taylor joint spectra

Abstract: In my talk, I will present recent progress on the operator side of multivariable Clark theory and explain how compressed shifts on model spaces in the bidisk can be perturbed to pairs of unitary operators. The perturbations involved are often infinite-dimensional, but under additional assumptions they admit fairly concrete descriptions. For rational inner functions, the Taylor joint spectrum of the resulting unitary operators is in turn identified with the support of Clark measures.

This reports on joint work with Palak Arora, Kelly Bickel, and Constanze Liaw.