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Almost Periodic Factorization Of Certain Block Triangular Matrix Functions, Ilya M. Spitkovsky, Darryl H. Yong

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Let

where , and . For rational such matrices are periodic, and their Wiener-Hopf factorization with respect to the real line always exists and can be constructed explicitly. For irrational , a certain modification (called an almost periodic factorization) can be considered instead. The case of invertible and commuting , was disposed of earlier-it was discovered that an almost periodic factorization of such matrices does not always exist, and a necessary and sufficient condition for its existence was found. This paper is devoted mostly to the situation when is not invertible but the commute pairwise (). The complete description is …