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Odd-order differential expressions with positive supporting coefficients

Published online by Cambridge University Press:  14 November 2011

Bernd Schultze
Affiliation:
Fachbereich 6-Mathematik, Universität GH Essen, Universitätsstrasse 3, 4300 Essen, F.R.G

Synopsis

The deficiency indices (mean deficiency index) and the essential spectrum for a class of odd order ordinary differential expressions are determined. The considered expressions are relatively bounded or relatively compact perturbations of symmetric expressions with odd order terms having as coefficients real powers of the independent variable.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Evans, W. D., Lewis, R. T. and Zettl, A.. Non-self-adjoint operators and their essential spectra. Proceedings of the Conference on Ordinary Differential Equations, Dundee 1982, LectureNotes in Mathematics 1032 (Berlin: Springer).Google Scholar
2Frentzen, H.. A limit-point criterion for real polynomials in symmetric quasi-differential expressions of arbitrary order. Quaestiones Math. 5 (1982), 83105.CrossRefGoogle Scholar
3Goldberg, S.. Unbounded linear operators (New York: McGraw-Hill, 1966).Google Scholar
4Hinton, D.. Deficiency indices of odd-order differential operators. Rocky Mountain J. Math. 8 (1978), 627640.CrossRefGoogle Scholar
5Kato, T.. Perturbation theory for linear operators (Berlin: Springer, 1966).Google Scholar
6Kauffman, R. M.. On the limit-n classification of ordinary differential operators with positive coefficients. Proc. London Math. Soc. 35 (1977), 496526.CrossRefGoogle Scholar
7Kauffman, R. M., Read, T. T. and Zettl, A.. The deficiency index problem for powers of ordinary differential expressions. Lecture Notes in Mathematics 621 (Berlin: Springer, 1977).Google Scholar
8Kwong, M. K. and Zettl, A.. Norm inequalities of product form in weighted Lp-spaces. Proc. Roy. Soc. Edinburgh Sect. A 89 (1981), 293307.CrossRefGoogle Scholar
9Mergler, B. and Schultze, B.. A perturbation method and the limit-point case of even ordersymmetric differential expressions. Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 121135.CrossRefGoogle Scholar
10Mergler, B. and Schultze, B.. On the stability of the limit-point property of “Kauffman expressions” under relatively bounded perturbations. Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), 7389.CrossRefGoogle Scholar
11Schultze, B.. A limit-point criterion for 2n-th order symmetric differential expressions. Proc. Roy. Soc. Edinburgh Sect. A 90 (1981), 112.CrossRefGoogle Scholar
12Schultze, B.. A limit-point criterion for even order symmetric differential expressions with positive supporting coefficients. Proc. London Math. Soc. (3) 46 (1983), 561576.CrossRefGoogle Scholar