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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

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