Relations on noncommutative variables and associated orthogonal polynomials

T. Banks, T. Constantinescu, J. L. Johnson

Published 2003-12-19Version 1

This semi-expository paper surveys results concerning three classes of orthogonal polynomials: in one non-hermitian variable, in several isometric non-commuting variables, and in several hermitian non-commuting variables. The emphasis is on some dilation theoretic techniques that are also described in some details.