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Generalised factorisation for a class of Jones form matrix functions*

Published online by Cambridge University Press:  14 November 2011

M. C. Câmara ,
A. B. Lebre  and
F.-O. Speck
M. C. Câmara
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal
A. B. Lebre
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal
F.-O. Speck
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal
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Synopsis

A systematic approach is proposed for the generalised factorisation of certain non-rational n × n matrix functions. The first main result consists in a transformation of a meromorphic into a generalised factorisation by algebraic means. It closes a gap between the classical Wiener-Hopf procedure and the operator theoretic method of generalised factorisation. Secondly, as examples we consider certain matrix functions of Jones form or of N-part form, which are equivalent to each other, in a sense. The factorisation procedure is complete and explicit, based only on the factorisation of scalar functions, of rational matrix functions and upon linear algebra. Applications in elastodynamic diffraction theory are treated in detail and in a most effective way.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 3 , 1993 , pp. 401 - 422
Copyright
Copyright © Royal Society of Edinburgh 1993

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