Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2002-09-30
Tensor Algebras and Displacement Structure II: Non-Commutative Szegö PolynomialsTiberiu Constantinescu and J. L. Johnson (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