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Factorization of matrix functions and their inverses via power product expansions

✍ Scribed by H. Gingold

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
262 KB
Volume
430
Category
Article
ISSN
0024-3795

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✦ Synopsis

The conversion of a power series with matrix coefficients into an infinite product of certain elementary matrix factors is studied. The expansion of a power series with matrix coefficients as the inverse of an infinite product of elementary factors is also analyzed. Each elementary factor is the sum of the identity matrix and a certain matrix coefficient multiplied by a certain power of the variable. The two expansions provide us with representations of a matrix function and its inverse by infinite products of elementary factors. Estimates on the domain of convergence of the infinite products are given.

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## Abstract This paper deals with what we call modified singular integral operators. When dealing with (pure) singular integral operators on the unit circle with coefficients belonging to a decomposing algebra of continuous functions it is known that a factorization of the symbol induces a factoriz