### Abstract

Problems of Nehari type are studied for matrix valued k-variable almost periodic Wiener functions: Find contractive k-variable almost periodic Wiener functions having prespecified Fourier coefficients with indices in a given halfspace of ℝ. We characterize the existence of a solution, give a construction of the solution set, and exhibit a particular solution that has a certain maximizing property. These results are used to obtain various distance formulas and multivariable almost periodic extensions of Sarason's theorem. In the periodic case, a generalization of Sarason's theorem is proved using a variation of the commutant lifting theorem. The main results are further applied to a model-matching problem for multivariable linear filters.

Original language | English (US) |
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Pages (from-to) | 3-35 |

Number of pages | 33 |

Journal | Journal of Operator Theory |

Volume | 47 |

Issue number | 1 |

State | Published - 2002 |

### Keywords

- Almost periodic matrix functions
- Band method
- Besikovitch space
- Commutant lifting
- Contractive extensions
- Hankel operators
- Model matching
- Sarason's Theorem

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*Journal of Operator Theory*,

*47*(1), 3-35.