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Discrete spectra criteria for singular differential operators with middle terms

Published online by Cambridge University Press:  24 October 2008

Don B. Hinton  and
Roger T. Lewis
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Extract

Let l be the differential operator of order 2n defined by

where the coefficients are real continuous functions and pn > 0. The formally self-adjoint operator l determines a minimal closed symmetric linear operator L0 in the Hilbert space L2 (0, ∞) with domain dense in L2 (0, ∞) ((4), § 17). The operator L0 has a self-adjoint extension L which is not unique, but all such L have the same continuous spectrum ((4), § 19·4). We are concerned here with conditions on the pi which will imply that the spectrum of such an L is bounded below and discrete.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 2 , March 1975 , pp. 337 - 347
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Eastham, M. S. P.The least limit point of the spectrum associated with singular differential operators. Proc. Cambridge Philos. Soc. 67 (1970), 277–281.CrossRefGoogle Scholar
(2)Glazman, I. M.Direct methods of qualitative spectral analysis of singular differential operators (I.P.S.T., Jerusalem, 1965).Google Scholar
(3)Lewis, R. T.The discreteness of the spectrum of self-adjoint, even order, one term, differential operators. Proc. Amer. Math. Soc. 42 (1974), 480–482.CrossRefGoogle Scholar
(4)Naimark, M. A., Linear differential operators: Part II (Ungar, New York, 1968).Google Scholar
(5)Rollins, L. W.Criteria for discrete spectrum of singular self-adjoint differential operators. Proc. Amer. Math. Soc. 34 (1972), 195–200.CrossRefGoogle Scholar