### Abstract

A factorability criterion is obtained constructively, and the respective factorization obtained explicitly, for 2 × 2 triangular almost periodic matrix functions of the form [(e_{λ}, 0; f, e_{- λ})]. Here f = c_{- 1} e_{- α} - c_{0} + c_{1} e_{β}, e_{μ} (x) : = e^{i μ x}, c_{j} are non-zero constants and 0 < α, β, α + β < λ ≤ α + β + max {α, β} with α / β 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.

Original language | English (US) |
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Pages (from-to) | 416-433 |

Number of pages | 18 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 367 |

Issue number | 2 |

DOIs | |

State | Published - Jul 15 2010 |

### Keywords

- Almost periodic factorization

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

Câmara, M. C., Karlovich, Y. I., & Spitkovsky, I. M. (2010). Constructive almost periodic factorization of some triangular matrix functions.

*Journal of Mathematical Analysis and Applications*,*367*(2), 416-433. https://doi.org/10.1016/j.jmaa.2010.01.052