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On a strong limit-point condition and an integral inequality associated with a symmetric matrix differential expression*

Published online by Cambridge University Press:  14 February 2012

D. A. R. Rigler
D. A. R. Rigler
Affiliation:
Department of Mathematics, University of Dundee
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Synopsis

This paper is concerned with some properties of an ordinary symmetric matrix differential expression M, denned on a certain class of vector-functions, each of which is defined on the real line. For such a vector-function F we have M[F] = −F“ + QF on R, where Q is an n × n matrix whose elements are reasonably behaved on R. M is classified in an equivalent of the limit-point condition at the singular points ± ∞, and conditions on the matrix coefficient Q are given which place M, when n> 1, in the equivalent of the strong limit-point for the case n = 1. It is also shown that the same condition on Q establishes the integral inequality for a certain class of vector-functions F.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 2 , 1977 , pp. 155 - 159
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Anderson, R. L.. Singular symmetric differential operators on a Hilbert space of vector valued functions (Univ. of Tennessee: Ph.D. Thesis, 1973).Google Scholar
2Everitt, W. N.. On an extension to an integro-differential inequality of Hardy, Littlewood and Pólya, Proc. Roy. Soc. Edinburgh Sect. A, 69 (1971), 23.Google Scholar
3Everitt, W. N. and Giertz, M.. A Dirichlet type result for ordinary differential operators. Math. Ann. 203 (1973), 119–128.CrossRefGoogle Scholar
4Hardy, G. H., Littlewood, J. E. and Pólya, G.. Inequalities (Cambridge: University Press, 1934).Google Scholar
5Lidskii, V.B.. On the number of solutions with integrable square of the system y” + Py = λy. Dokl. Akad. Nauk. SSSR 95 (1954), 217–220.Google Scholar
6Rigler, D. A. R.. Eigenvalue problems for systems of linear ordinary differential equations (Dundee: Univ. Ph.D. Thesis, 1975).Google Scholar