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Singular differential operators with spectra discrete and bounded below

Published online by Cambridge University Press:  14 November 2011

Don B. Hinton  and
Roger T. Lewis
Don B. Hinton
Affiliation:
Mathematics Department, University of Tennessee, Knoxville, Tennessee 37916, U.S.A.
Roger T. Lewis
Affiliation:
Mathematics Department, University of Alabama in Birmingham, Alabama 35294, U.S.A.
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Synopsis

A weighted, formally self-adjoint ordinary differential operator l of order 2n is considered, and conditions are given on the coefficients of l which ensure that all self-adjoint operators associated with l have a spectrum which is discrete and bounded below. Both finite and infinite singularities are considered. The results are obtained by the establishment of certain conditions which imply that l is non-oscillatory.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 1-2 , 1979 , pp. 117 - 134
Copyright
Copyright © Royal Society of Edinburgh 1979

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