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