### Abstract

Using an abbreviation e? to denote the function ei?x on the real line R, let G=[e?0fe??], where f is a linear combination of the functions e?, e?, e???, e??? with some (0<)?,?<?. 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.

Original language | English (US) |
---|---|

Pages (from-to) | 625-640 |

Number of pages | 16 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 376 |

Issue number | 2 |

DOIs | |

State | Published - Apr 15 2011 |

### Fingerprint

### Keywords

- Almost periodic factorization

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*376*(2), 625-640. https://doi.org/10.1016/j.jmaa.2010.11.037

**Constructive factorization of some almost periodic triangular matrix functions with a quadrinomial off diagonal entry.** / Bastos, M. A.; Bravo, A.; Karlovich, Yu I.; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 376, no. 2, pp. 625-640. https://doi.org/10.1016/j.jmaa.2010.11.037

}

TY - JOUR

T1 - Constructive factorization of some almost periodic triangular matrix functions with a quadrinomial off diagonal entry

AU - Bastos, M. A.

AU - Bravo, A.

AU - Karlovich, Yu I.

AU - Spitkovsky, Ilya

PY - 2011/4/15

Y1 - 2011/4/15

N2 - Using an abbreviation e? to denote the function ei?x on the real line R, let G=[e?0fe??], where f is a linear combination of the functions e?, e?, e???, e??? with some (0<)?,?<?. 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.

AB - Using an abbreviation e? to denote the function ei?x on the real line R, let G=[e?0fe??], where f is a linear combination of the functions e?, e?, e???, e??? with some (0<)?,?<?. 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.

KW - Almost periodic factorization

UR - http://www.scopus.com/inward/record.url?scp=78650707290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650707290&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2010.11.037

DO - 10.1016/j.jmaa.2010.11.037

M3 - Article

VL - 376

SP - 625

EP - 640

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -