# Constanze Liaw: Generalizations of Aleksandrov-Clark theory

**Time: **
Wed 2019-05-29 15.30

**Lecturer: **
Constanze Liaw (University of Dalaware)

**Location: ** Room 32, building 5, Kräftriket, Department of Mathematics, Stockholm University ￼

Sammanfattning:

In the 1950s, Clark developed a connection between complex function theory and unitary rank-one perturbations that have purely singular spectrum. The Herglotz representation theorem provides a bijection between analytic contractions on the unit disc of the complex plane and families of Aleksandrov-Clark measures, which are the spectral measures of the perturbed operators. More recently, two primary directions for generalizations have been investigated: matrix-valued analytic contractions (and finite-rank perturbations), as well as functions of several variables (and Cuntz-Toeplitz operator systems).