  We formulate a conjecture concerning spectral factorization of a class of
trigonometric polynomials of two variables and prove it for special cases. Our
method uses relations between the distribution of values of a polynomial of two
variables and the distributions of values of an associated family of
polynomials of one variable. We suggest an approach to prove the full
conjecture using relations between the distribution of values and the
distribution of roots of polynomials.
