Welcome to Analysis

Analysis is that branch of mathematics which evolved from the notions of approximations, limits and continuity of real- and complex-valued functions. While the fundamental theorem of calculus remains to this day one of the central pillars of mathematics, modern analysis deals with the above concepts in broader and more abstract settings such as those of topological groups and algebras.

Events

Friday, February 3, 2023 3:00 pm - 4:00 pm EST

Non-commutative measure theory

Robert Martin, University of Manitoba

Measure theory on the complex unit circle and analytic function theory in the unit disk, in particular the theory of Hardy spaces, are fundamentally connected. Several celebrated theorems due to P. Fatou, G. Herglotz, F. and M. Riesz and G. Szego describe the relationship between these theories. We will show that many of these classical results have natural extensions to the multivariate and non-commutative settings of the full Fock space, or free Hardy space of square–summable power series in several non-commuting variables and positive non-commutative (NC) measures. Here a (positive) NC measure is any positive linear functional on the free disk system, the operator system generated by the left creation operators, which act as left multiplication by the independent NC variables on the free Hardy space. We will focus on a recently established NC Szego theorem and its consequences.

This seminar will be held both online and in person: