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Some remarks on a paper by W. N. Everitt

Published online by Cambridge University Press:  14 February 2012

K. Daho  and
H. Langer
K. Daho
Affiliation:
Uppsala University, Sweden
H. Langer
Affiliation:
Technical University, Dresden, G.D.R.
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Extract

Everitt has shown [1[, that for α ∊ [0, π/2] the undernoted problem (1.1–2) with an indefinite weight function r can be represented by a selfadjoint operator in a suitable Hilbert space. This result is extended to arbitrary α ∊ [0, π), replacing the Hilbert space in some cases by a Pontrjagin space with index one. The problem is also treated in the Krein space generated by the weight function r.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 1-2 , 1977 , pp. 71 - 79
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Everitt, W. N. Some remarks on a differential expression with an indefinite weight function. In Spectral theory and asymptotics of differential equations. Math. Stud., 13 (Amsterdam: North-Holland, 1974).Google Scholar
2Bognar, J.Indefinite inner product spaces (Berlin: Springer, 1974).CrossRefGoogle Scholar
3Krein, M. G. and Langer, H.Defect subspaces and generalised resolvents of a Hermitean operator in the space IIx. Functional Anal. Appl. 5 (1972), 136–146.Google Scholar
4Daho, K. and Langer, H.Sturm-Liouville operators with an indefinite weight function. Proc. Roy. Soc. Edinburgh Sect. A 78 (1977), 161–191.CrossRefGoogle Scholar