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VII.—On the Spectrum of Ordinary Second Order Differential Operators.*

Published online by Cambridge University Press:  14 February 2012

Jyoti Chaudhuri  and
W. N. Everitt
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Synopsis

This paper considers properties of the spectrum of differential operators derived from differential expressions of the second order. The object is to link the spectral properties of these differential operators with the analytic, function-theoretic properties of the solutions of the differential equation. This provides an alternative approach to the spectral theory of these differential operators but one which is consistent with the standard definitions used in Hilbert space theory. In this way the approach may be of interest to applied mathematicians and theoretical physicists.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 68 , Issue 2 , 1969 , pp. 95 - 119
Copyright
Copyright © Royal Society of Edinburgh 1969

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References

References to Literature

1.Akhiezer, N. I. and Glazman, I. M., 1961. Theory of linear operators in Hilbert Space. Vols. I & II. New York: Ungar.Google Scholar
2.Coddington, E. A., and Levinson, N., 1955. Theory of ordinary differential equations. New York: McGraw Hill.Google Scholar
3.Coddington, E. A., 1951. “On the nature of the spectrum of singular second-order linear differential equations”, Can. J. Math., 3, 335–338.CrossRefGoogle Scholar
4.Dunford, N., and Schwartz, J. T., 1963. Linear operators Part II. Spectral theory: Self-adjoint operators in Hilbert Space. New York: Interscience.Google Scholar
5.Everitt, W. N., 1963. “On the self-adjoint domains of second-order differential equations”, Q. Jl Math., 14, 41–45.CrossRefGoogle Scholar
6.Naimark, M. A., 1968. Linear differential operators. New York: Ungar. (German edition : Berlin: Akademie-Verlag, 1960.)Google Scholar
7.Titchmarsh, E. C., 1962. Eigenfunction expansions associated with second order differential equations: Part I. O.U.P.CrossRefGoogle Scholar
8.Titchmarsh, E. C., 1958. Ibid, Part II. O.U.P.Google Scholar
9.Kodaira, K., 1949. “The Eigenvalue problem for ordinary differential equations of the second order and Heisenbergs theory of matrices”, Am. J. Math., 71, 921–945.CrossRefGoogle Scholar
10.Gelfand, I. M., and Levitan, B. M., 1955. “On the determination of a differential equation from its spectral function”, Am. Math. Soc. Transl., 1.Google Scholar