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Regularly solvable extensions of non-self-adjoint ordinary differential operators

Published online by Cambridge University Press:  14 November 2011

W. D. Evans
W. D. Evans
Affiliation:
Pure Mathematics Department, University College, Cardiff CF1 1XL
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Synopsis

Let L0, M0 be closed densely defined linear operators in a Hilbert space H which form an adjoint pair, i.e. . In this paper, we study closed operators S which satisfy and are regularly solvable in the sense of Višik. The abstract results obtained are applied to operators generated by second-order linear differential expressions in a weighted space L2(a, b; w).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 79 - 95
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Calkin, J. W.. Symmetric transformations in Hilbert space. Duke Math. J. 7 (1940), 504–508.CrossRefGoogle Scholar
2Coddington, E. A. and Levinson, N.. Theory of ordinary differential equations (New York: McGraw-Hill, 1955).Google Scholar
3Galindo, A.. On the existence of J -self-adjoint extensions of J -symmetric operators with adjoint. Comm. Pure Appl. Math. 15 (1962), 423–425.CrossRefGoogle Scholar
4Kato, T.. Perturbation theory of linear operators (Berlin: Springer, 1966).Google Scholar
5Knowles, I.. On J -self-adjoint extensions of J -symmetric operators. Proc. Amer. Math. Soc. 79 (1980), 42–44.Google Scholar
6Knowles, I.. On the boundary conditions characterizing J -self-adjoint extensions of J -symmetric operators. J. Differential Equations 40 (1981), 193–216.CrossRefGoogle Scholar
7Naimark, M. A.. Linear differential operators, Part II (London: Harrap, 1968).Google Scholar
8Sims, A. R.. Secondary conditions for linear differential operators of the second order. J. Math. Mech. 6 (1957), 247–285.Google Scholar
9Višik, M. I.. On general boundary problems for elliptic differential equations. Amer. Math. Soc. Transl. (2), 24 (1963), 107–172.Google Scholar
10Zhikhar, N. A.. The theory of extensions of J -symmetric operators. Ukrain. Mat. Ž. 9 (4) (1959), 352–364.Google Scholar