Tensor algebras and displacement structure. II. Noncommutative Szego polynomials

Details Tensor algebras and displacement structure. II. Noncommutative Szego polynomials Tensor algebras and displacement structure. II. Noncommutative Szego polynomials

2002-01-22

arxiv.org/abs/math/0201213v1

Mathematics

Functional Analysis

17 pages

Scientific paper

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 Szego type theory of orthogonal polynomials in the unit circle for several noncommuting variables. Thus, we obtain the recurrence equations and Christoffel-Darboux type formulas, as well as a Favard type result. Also we continue to study a Szego kernel for the N-dimnesional unit ball of an infinite dimensional Hilbert space.

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