Continuous spectrum and square-integrable solutions of differential operators with intermediate deficiency index |
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Authors: | Jiong Sun |
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Institution: | a Math. Department, Inner Mongolia University, Hohhot 010021, China b Math. Department, Tianjin University of Science and Technology, Tianjin 300222, China c Math. Department, Northern Illinois University, DeKalb, IL 60115, USA |
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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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Keywords: | Differential operators Intermediate deficiency indices Continuous spectrum Square-integrable solutions Singular boundary conditions |
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