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18.—Asymptotic Estimates for the Lengths of the Gaps in the Essential Spectrum of Self-adjoint Differential Operators

Published online by Cambridge University Press:  14 February 2012

M. S. P. Eastham  and
W. N. Everitt
M. S. P. Eastham
Affiliation:
Chelsea College, University of London
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Synopsis

The paper gives asymptotic estimates of the form

as λ→∞ for the length l(μ)of a gap, centre μ in the essential spectrum associated with second-order singular differential operators. The integer r will be shown to depend on the differentiability properties of the coefficients in the operators and, in fact, r increases with the increasing differentiability of the coefficients. The results extend to all r ≧ – 2 the long-standing ones of Hartman and Putnam [10], who dealt with r = 0, 1, 2.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 74 , 1976 , pp. 239 - 252
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

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Additional reference:

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