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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 3, 2002, pp. 611–626
DOI: 10.4171/ZAA/1098

Published online: 2002-09-30

Tensor Algebras and Displacement Structure II: Non-Commutative Szegö Polynomials

Tiberiu Constantinescu[1] and J. L. Johnson[2]

(1) University of Texas at Dallas, United States
(2) University of Texas at Dallas, Richardson, USA

In this paper we continue to explore the connection between tensor algebras and displacement structure. We focus on recursive orthonormalization and we develop an analogue of the Szegö-type theory of orthogonal polynomials in the unit circle for several non-commuting variables. Thus we obtain recurrence equations and Christoffel-Darboux formulas for Szegö polynomials in several non-commuting variables, as well as a Favard type result. Also, we continue to study a Szegö-type kernel for the $N$-dimensional unit ball of an infinite-dimensional Hilbert space.

Keywords: Displacement structure, tensor algebras, Szegö polynomials

Constantinescu Tiberiu, Johnson J.: Tensor Algebras and Displacement Structure II: Non-Commutative Szegö Polynomials. Z. Anal. Anwend. 21 (2002), 611-626. doi: 10.4171/ZAA/1098