Almost periodic factorization of block triangular matrix functions revisited

Let G be an n x n almost periodic (AP) matrix function defined on the real line R. By the AP factorization of G we understand its representation in th e form G = G(+)Lambda G(-), where GS(+)(+/-1)(G(-)(+/-1)) is an AP matrix f unction with all Fourier exponents of its entries being non-negative (respe ctively, non-positive) and Lambda(x) = diag[e(i lambda lx), ..., e(i lambda nx)], lambda(l), ..., lambda(n), is an element of R. This factorization pl ays an important role in the consideration of systems of convolution type e quations on unions of intervals. In particular, systems of m equations on o ne interval of length lambda lead to AP factorization of matrices. [GRAPHICS] We develop a factorization techniques for matrices of the form (0.1) under various additional conditions on the off-diagonal block f. The cases covere d include f with the Fourier spectrum Omega(f) lying on a grid (Omega(f) su bset of -nu + hZ) and the trinomial f (Omega(f) = {-nu, mu, alpha}) with -n u < mu < alpha, alpha + \mu\ + nu greater than or equal to lambda. (C) 1999 Published by Elsevier Science Inc. All rights reserved.