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arXiv · 2608.23073

Addendum to "Factoring non-negative operator valued trigonometric polynomials in two variables"

Michael A. Dritschel·Igor Klep·Scott McCullough·Jurij Volčič
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Abstract

Factorization for positive semidefinite matrix-valued polynomials over a nonsingular compact affine real surface is established. Corollaries include Fej\'er-Riesz factorization for bivariate matrix polynomials that take positive semidefinite values and resolutions to questions posed by Mehta-Slofstra-Zhao and Savchuk-Schm\"udgen. An explicit example shows a conclusion of [Dri25, Theorem, p. 519] that arises organically from its proof need not hold. The difficulty is traced to [Dri25, Theorem 3.7].

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Michael A. Dritschel, Igor Klep, Scott McCullough, Jurij Volčič. 2026-08-24. Addendum to "Factoring non-negative operator valued trigonometric polynomials in two variables". https://arxiv.org/abs/2608.23073

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