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A factorisation procedure for two by two matrix functions on the circle with two rationally independent entries

Published online by Cambridge University Press:  14 November 2011

S. Prößdorf  and
F.-O. Speck
S. Prößdorf
Affiliation:
Karl-Weierstrass-Institut für Mathematik, Akademie der Wissenschaften der DDR, Mohrenstrasse 39, 1086 Berlin, G.D.R.
F.-O. Speck
Affiliation:
Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, 6100 Darmstadt, F.R.G.
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Synopsis

The aim of this paper is the explicit canonical or standard factorisation of matrix functions with Wiener algebra elements. The present approach covers all regular 2 × 2 matrices where two entries are arbitrary and the remaining two are linear combinations of the former with rational coefficient functions. It is based on the knowledge of how to factorise scalar functions and rational matrix functions. In general, one also needs the approximation of any scalar Wiener algebra function with a rational function. However, this can be easily circumvented in many applications by intuitive manipulations with rational matrix functions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 1-2 , 1990 , pp. 119 - 138
Copyright
Copyright © Royal Society of Edinburgh 1990

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