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On some properties of matrices associated with linear ordinary quasi-differential expressions

Published online by Cambridge University Press:  14 November 2011

W. N. Everitt
Affiliation:
Department of Mathematics, University of Birmingham, P.O. Box 363, Birmingham B15 2TT
Jennifer D. Key
Affiliation:
Department of Mathematics, University of Birmingham, P.O. Box 363, Birmingham B15 2TT

Synopsis

In the general theory of ordinary linear quasi-differential equations, the set of Shin–Zettl matrices plays an important role. This paper displays certain properties of these matrices and their behaviour under a special form of transformation. Essentially, the problems can be considered within the framework of linear algebra.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Everitt, W. N. and Neuman, F..A concept of adjointness and symmetry of differential expressions based on the generalised Lagrange identity and Green formula. To appear in the Proceedings of the 1982 Dundee Symposium on Ordinary Differential Equations (Berlin: Springer).Google Scholar
2Everitt, W. N. and Zettl, A.. Generalized symmetric ordinary differential expressions I: the general theory. Nieuw Arch. Wisk. 27 (1979), 362397.Google Scholar
3Naimark, M. A.. Linear differential operators (New York: Ungar Part 1, 1967; Part II, 1968).Google Scholar
4Morris, A. O.. Linear algebra: an introduction 2nd edn (New York: Van Nostrand, 1982).Google Scholar
5Zettl, A.. Formally self-adjoint quasi-differential operators. Rocky Mountain J. Math. 5 (1975), 453474.CrossRefGoogle Scholar