Tensor algebras and displacement structure. III: Asymptotic properties (Q1884377)

The authors' goal is to extend the results to the class of orthogonal polynomials in several noncommuting variables introduced in part II by [\textit{T. Constantinescu} and \textit{J. L. Johnson} [ibid. 21, No. 3, 611--626 (2002; Zbl 1028.15030)]. The paper is organized as follows. In Section 2 they review notation and a framework for studying orthogonal polynomials associated to polynomial relations on several noncommuting variables. In Section 3 they analyze the case of no relation in dimension one. In Section 4 they discuss a few examples such as polynomials on the unit circle, polynomials on the real line and Szegő polynomials in several noncommuting variables.