### 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) |
---|---|

Pages (from-to) | 1148-1173 |

Number of pages | 26 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 432 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 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

**Toeplitz operators of finite interval type and the table method.** / Câmara, M. C.; Diogo, C.; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 432, no. 2, pp. 1148-1173. https://doi.org/10.1016/j.jmaa.2015.07.028

}

TY - JOUR

T1 - Toeplitz operators of finite interval type and the table method

AU - Câmara, M. C.

AU - Diogo, C.

AU - Spitkovsky, Ilya

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We solve a Riemann-Hilbert problem with almost periodic coefficient G, associated to a Toeplitz operator TG 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 TG. Some unexpected properties of the Fourier spectrum of the solutions are revealed which are not apparent through other approaches to the same problem.

AB - We solve a Riemann-Hilbert problem with almost periodic coefficient G, associated to a Toeplitz operator TG 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 TG. Some unexpected properties of the Fourier spectrum of the solutions are revealed which are not apparent through other approaches to the same problem.

KW - Almost periodic function

KW - Factorization theory

KW - Riemann-Hilbert problem

KW - Toeplitz operator

UR - http://www.scopus.com/inward/record.url?scp=84939259768&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939259768&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2015.07.028

DO - 10.1016/j.jmaa.2015.07.028

M3 - Article

VL - 432

SP - 1148

EP - 1173

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -