POSITIVE EXTENSIONS OF MATRIX FUNCTIONS OF 2 VARIABLES WITH SUPPORT IN AN INFINITE BAND

Let Delta be a band in Z(2) bordered by two parallel lines that are of equal distance to the origin. Given a positive definite l(1) sequence of matrices {c(j)}(j is an element of Delta), we prove that there is a positive definite matrix function f in the Wiener algebra of the bit orus such that the Fourier coefficients verifies (f) over cap(k) = c(k ) for every k is an element of Delta. We also prove that among all mat rix functions with these properties there exists a distinguished one t hat maximizes the entropy.