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It is shown using Schur complement techniques that on finite dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in two variables with degree (d₁,d₂) ( d 1 , d 2 ) can be written as a sum of hermitian squares of at most 2d₂ 2 d 2 analytic polynomials.
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Michael A. Dritschel (2024) studied this question.
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