Abstract
We now begin with studying AP factorization for special classes of almost periodic matrix functions. The Portuguese transformation is a procedure of reducing the factorization problem for one matrix function to another one which is often simpler than the original matrix function. Repeated application of the Portuguese transformation may therefore lead to a matrix function which is easily factorable. The Portuguese transformation is based on the solution of a special corona theorem. This corona problem will be studied in detail in this chapter.
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