#### Title

Constructive factorization of some almost periodic triangular matrix functions with a quadrinomial off diagonal entry

#### Document Type

Article

#### Department/Program

Mathematics

#### Journal Title

Journal of Mathematical Analysis and Applications

#### Pub Date

2011

#### Volume

376

#### Issue

2

#### First Page

625

#### Abstract

Using an abbreviation e(mu) to denote the function e(i mu x) on the real line R, let G = [(e lambda)(f) (0)(e-lambda)], where f is a linear combination of the functions e(alpha), e(beta), e(alpha-lambda), e(beta-lambda) with some (0 <) alpha, beta < lambda. The criterion for G to admit a canonical factorization was established recently by Avdonin, Bulanova and Moran (2007) [1]. We give an alternative approach to the matter, proving the existence (when it does take place) via deriving explicit factorization formulas. The non-existence of the canonical factorization in the remaining cases then follows from the continuity property of the geometric mean. (C) 2010 Elsevier Inc. All rights reserved.

#### Recommended Citation

Spitkovsky, I. M.; Bastos, M. A.; Bravo, A.; and Karlovich, Yu I., Constructive factorization of some almost periodic triangular matrix functions with a quadrinomial off diagonal entry (2011). *Journal of Mathematical Analysis and Applications*, 376(2), 625-640.

10.1016/j.jmaa.2010.11.037

#### DOI

10.1016/j.jmaa.2010.11.037