Some Classes of Factorable Matrix Functions

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 L_p 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.