### Abstract

It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener-Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.

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

Pages (from-to) | 3188-3207 |

Number of pages | 20 |

Journal | Journal of Functional Analysis |

Volume | 255 |

Issue number | 11 |

DOIs | |

State | Published - Dec 1 2008 |

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### Keywords

- Almost periodic functions
- Factorization
- Hermite rings
- Matrix functions
- Toeplitz corona
- Wiener algebra

### ASJC Scopus subject areas

- Analysis

### Cite this

**Algebras of almost periodic functions with Bohr-Fourier spectrum in a semigroup : Hermite property and its applications.** / Rodman, Leiba; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Journal of Functional Analysis*, vol. 255, no. 11, pp. 3188-3207. https://doi.org/10.1016/j.jfa.2008.05.010

}

TY - JOUR

T1 - Algebras of almost periodic functions with Bohr-Fourier spectrum in a semigroup

T2 - Hermite property and its applications

AU - Rodman, Leiba

AU - Spitkovsky, Ilya

PY - 2008/12/1

Y1 - 2008/12/1

N2 - It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener-Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.

AB - It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener-Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.

KW - Almost periodic functions

KW - Factorization

KW - Hermite rings

KW - Matrix functions

KW - Toeplitz corona

KW - Wiener algebra

UR - http://www.scopus.com/inward/record.url?scp=54949153752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54949153752&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2008.05.010

DO - 10.1016/j.jfa.2008.05.010

M3 - Article

VL - 255

SP - 3188

EP - 3207

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 11

ER -