On spectral factorization in two-dimensions

Implications of the (partial) feasibility of spectral factorability of two-dimensions (2D) parahermitian polynomial matrices, nonnegative on the unit bidisc, are explored. Specifically, we consider three issues connected with the problem of spectral factorization in two dimensions and investigate their relationship in the light of the 2D spectral factorability result mentioned. These are the extendability of 2D positive definite correlation sequences from a finite section of them, the network theoretic interpretations of parameterizations of extensions along with maximum entropy extension and finally the stochastic realization problem in 2D. The intent is not so much to present solutions but exposition of the issues.