Abstract
This chapter deals with various applications and results on generalized factorization of matrix functions. It is shown that any non-singular continuous matrix function admits a generalized factorization relative to any Lp(Γ) (D (l<p<∞). This result is contrasted to the case of non-singular piecewise continuous matrix functions which, in general, admit factorization relative to Lp(Γ) only for certain values of p and have partial indices depending on p . An application of generalized factorization to a basis problem in L2 is presented. Earlier results on factorization of dissipative and self-adjoint matrix functions are generalized. In the final section factorization relative to Lp(Γ) is considered as a separate case.
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