Kernels of Asymmetric Toeplitz Operators and Applications to Almost Periodic Factorization

Necessary and sufficient factorability conditions are established for some new classes of almost periodic matrix functions, and explicit factorization formulas are given whenever the factorization exists. The results are based on the connection between factorability and properties of solutions to a related homogeneous Riemann–Hilbert problem. These solutions, in their turn, are described completely, for the cases at hand, via introduction and consideration of certain asymmetric Toeplitz operators.