Local and global factorizations of matrix-valued functions

Authors:
K. F. Clancey and I. Gohberg

Journal:
Trans. Amer. Math. Soc. **232** (1977), 155-167

MSC:
Primary 47G05; Secondary 45E05

DOI:
https://doi.org/10.1090/S0002-9947-1977-0454742-4

MathSciNet review:
0454742

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *C* be a simple closed Liapounov contour in the complex plane and *A* an invertible matrix-valued function on *C* with bounded measurable entries. There is a well-known concept of factorization of the matrix function *A* relative to the Lebesgue space . The notion of local factorization of *A* relative to at a point in *C* is introduced. It is shown that *A* admits a factorization relative to if and only if *A* admits a local factorization relative to at each point in *C*. Several problems connected with local factorizations relative to are raised.

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DOI:
https://doi.org/10.1090/S0002-9947-1977-0454742-4

Keywords:
Operator factorizations,
systems of singular integral equations

Article copyright:
© Copyright 1977
American Mathematical Society