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Characterisation of the factors of quasi-differential expressions

Published online by Cambridge University Press:  14 November 2011

D. Race  and
A. Zettl
D. Race
Affiliation:
Department of Mathematical and Computing Sciences, Guildford, Surrey GU2 5XH, U.K.
A. Zettl
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, U.S.A.
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Synopsis

A necessary and sufficient condition for a general, scalar, quasi-differential expression of order n to be factorisable into a product of expressions of order n − k and k, for any 0 < k < n, is given. The factors are characterised completely in terms of elements of the null space of the expression and its adjoint. The results obtained extend existing results due to both Polya and Zettl from the case of classical linear differential expressions to quasi-differential expressions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 3-4 , 1992 , pp. 297 - 312
Copyright
Copyright © Royal Society of Edinburgh 1992

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