Outer factorizations in one and several variables

2004/03/04 by Michael A. Dritschel, Dritschel, Michael A., Hugo J. Woerdeman +1 · 2 citations
Computer Science · Mathematics · #47A68 #47B35 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials #Matrix Theory and Algorithms #Optimization and Control (math.OC) #math.FA #math.OC #msc:47A68 #msc:47B35

paper · pdf · doi:10.48550/arxiv.math/0403099

19 pages

arxiv created 2004/03/04 · openalex publication_date 2004/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A multivariate version of Rosenblum's Fejer-Riesz theorem on outer factorization of trigonometric polynomials with operator coefficients is considered. Due to a simplification of the proof of the single variable case, new necessary and sufficient conditions for the multivariable outer factorization problem are formulated and proved.

Cited by

• Fejér--Riesz factorization for positive noncommutative trigonometric polynomials
• Positive operator-valued noncommutative polynomials are squares

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