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Lower Bounds for the Essential Spectrum of Fourth-Order Differential Operators

Published online by Cambridge University Press:  20 November 2018

Kurt Kreith
Kurt Kreith*
Affiliation:
University of California, Davis, California
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In this paper, we seek to determine the greatest lower bound of the essential spectrum of self-adjoint singular differential operators of the form

1

where 0 ≦ x < ∞. In the event that this bound is + ∞, our results will yield criteria for the discreteness of the spectrum of (1).

Such bounds have been established by Friedrichs (3) for Sturm-Liouville operators of the form

and our techniques will be closely related to those of (3). However, instead of studying the solutions of

2

directly, we shall exploit the intimate connection between the infimum of the essential spectrum of (1) and the oscillation properties of (2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 460 - 465
Copyright
Copyright © Canadian Mathematical Society 1969

References

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