### Abstract

We solve a Riemann-Hilbert problem with almost periodic coefficient G, associated to a Toeplitz operator T_{G} in a class which is closely connected to finite interval convolution equations, based on a generalization of the so-called table method. The explicit determination of solutions to that problem allows one to establish necessary and sufficient conditions for the invertibility of the corresponding Toeplitz operator, and to determine an appropriate factorization of G, providing explicit formulas for the inverse of T_{G}. Some unexpected properties of the Fourier spectrum of the solutions are revealed which are not apparent through other approaches to the same problem.

Original language | English (US) |
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Pages (from-to) | 1148-1173 |

Number of pages | 26 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 432 |

Issue number | 2 |

DOIs | |

State | Published - Dec 15 2015 |

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### Keywords

- Almost periodic function
- Factorization theory
- Riemann-Hilbert problem
- Toeplitz operator

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*432*(2), 1148-1173. https://doi.org/10.1016/j.jmaa.2015.07.028