Tensor algebras and displacement structure. II. Noncommutative Szego polynomials

2002/01/22 by T. Constantinescu, J. L. Johnson, Constantinescu, T. +1 · 2 citations
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.math/0201213

17 pages

arxiv created 2002/01/22 · arxiv updated 2009/11/30

Abstract

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.

Cited by

• Orthogonal Polynomials, Verblunsky Coefficients, and a Szegő-Verblunsky Theorem on the Unit Sphere in ℂ^d
• A Noncommutative Szegő-Type Theorem on the Row-Ball

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