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

What the math gives to ML

The paper establishes a multivariate Fejer-Riesz theorem: every positive-semidefinite bivariate matrix Laurent polynomial on the torus admits an analytic polynomial Gram factorization A = B*B. This can parameterize multi-channel convolutional operators whose Fourier response is positive semidefinite at every spatial frequency, avoiding sampled spectral penalties or post-hoc eigenvalue projections. The most direct transfer is a constrained CNN or diffusion-like residual block implemented as a learned filter bank followed by its adjoint.