Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591676 | Journal of Functional Analysis | 2008 | 20 Pages |
Abstract
We explore the connection between square-integrable solutions for real-values of the spectral parameter λ and the continuous spectrum of self-adjoint ordinary differential operators with arbitrary deficiency index d. We show that if, for all λ in an open interval I, there are d of linearly independent square-integrable solutions, then for every extension of Dmin the point spectrum is nowhere dense in I, and there is a self-adjoint extension of Smin which has no continuous spectrum in I. This analysis is based on our construction of limit-point (LP) and limit-circle (LC) solutions obtained recently in an earlier paper.
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