Outer factorizations in one and several variables

Dritschel, Michael; Woerdeman, Hugo

doi:10.1090/S0002-9947-05-03814-6

Outer factorizations in one and several variables
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by Michael A. Dritschel and Hugo J. Woerdeman

Trans. Amer. Math. Soc. 357 (2005), 4661-4679

DOI: https://doi.org/10.1090/S0002-9947-05-03814-6

Published electronically: June 21, 2005

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Abstract:

A multivariate version of Rosenblum’s Fejér-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.

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