Abstract
In this chapter we consider the factorization problem for some special classes of matrix functions with specific analytic properties. In Section 5.1 the criterion of Ф-factorability in Lp of matrix functions of the classes \({\text{L}}_\infty ^ \pm + {\text{C}}\) will be derived. Section 5.2 is dedicated to the factorization in some Banach algebras of functions, and in Section 5.3 we shall study the Ф-factorization of piecewise continuous matrix functions. The consideration of classes of special matrix functions is useful by making general factorability and Ф-factorability criteria proved in the previous more precise. Moreover, via this approach we are able to clarify some principal facts of factorization theory.
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