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The point-continuous spectrum of second-order, ordinary differential operators

Published online by Cambridge University Press:  14 November 2011

Christine Thurlow
Affiliation:
121 The Grove, Ealing, London W5

Synopsis

Given any countably infinite set of isloated points on the ℷ -axis, it is shown that there is a continuous q(x) such that these points constitute exactly the point-continuous spectrum for the equation yn″(x) + (ℷ —q(x))y(x) = 0(0≦x<∞) with some homogenous boundary condition at x = 0. This extends a result given by Eastham and McLeod for countably infinite sets of isolated points on the positive ℷ-axis.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

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