Local and global factorizations of matrixvalued functions
Authors:
K. F. Clancey and I. Gohberg
Journal:
Trans. Amer. Math. Soc. 232 (1977), 155167
MSC:
Primary 47G05; Secondary 45E05
MathSciNet review:
0454742
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Abstract: Let C be a simple closed Liapounov contour in the complex plane and A an invertible matrixvalued function on C with bounded measurable entries. There is a wellknown 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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 H. Röhrl, On holomorphic families of fiber bundles over the Riemann Sphere, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 33 (1960/61), 435477. MR 24 #A1728. MR 0131881 (24:A1728)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197704547424
PII:
S 00029947(1977)04547424
Keywords:
Operator factorizations,
systems of singular integral equations
Article copyright:
© Copyright 1977 American Mathematical Society
