Contractive Extension Problems for Matrix Valued Almost Periodic Functions of Several Variables

Problems of Nehari type are studied for matrix valued k-variable almost periodic Wiener functions: Find contractive k-variable almost periodic Wiener functions having prespeciied Fourier coeecients with indices in a given halfspace of R k. 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 multi-variable almost periodic extensions of Sarason's theorem. In the periodic case, a generalization of Sarason's theorem is proved using a variation of the commu-tant lifting theorem. The main results are further applied to a model-matching problem for multivariable linear lters.