Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Free Probability & Random Matrices Seminar


Tuesday, January 23rd, 2018

Time: 3:30-5:00 p.m.  Place: Jeffery Hall 319

Speaker: Rob Martin (University of Cape Town)

Title: Non-commutative Clark measures for Free and Abelian multi-variable Hardy space

Abstract:  In classical Hardy space theory, there is a natural bijection between the Schur class of contractive analytic functions in the complex unit disk and Aleksandrov- Clark measures on the unit circle. A canonical several-variable analogue of Hardy space is the Drury-Arveson space of analytic functions in the unit ball of d-dimensional complex space, and the canonical non-commuting or free multi- variable analogue of Hardy space is the full Fock space over d-dimensional complex space. Here, the full Fock space is naturally identified with a non- commutative reproducing kernel Hilbert space of free or non-commutative ana- lytic functions acting on a several-variable non-commutative open unit ball. We will extend the concept of Aleksandrov-Clark measure, the bijection between the Schur class and AC measures, Clark’s unitary perturbations of the shift, Lebesgue decomposition formulas and additional related results from one to several commuting and non-commuting variables.

Free Probability and Random Matrices Seminar Webpage: