Constructive almost periodic factorization of some triangular matrix functions

I. M. Spitkovsky, William & Mary
M. C. Camara
Yu. I. Karlovich

Abstract

A factorability criterion is obtained constructively, and the respective factorization obtained explicitly, for 2 x 2 triangular almost periodic matrix functions of the form [(e lambda)(f) (0)(e-lambda)]. Here f = c(-1)e(-alpha)-c(0)+c(1)e(beta), e(mu)(x) := e(i mu x), c(j) are non-zero constants and 0 < alpha, beta, alpha + beta < lambda <= alpha + beta + max{alpha, beta} with alpha/beta being irrational. Note that the factorization problem, even for triangular matrix functions as above with an arbitrary trinomial f, is open. The result obtained is yet another step towards its solution. (C) 2010 Elsevier Inc. All rights reserved.