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25.—Spectrum of a Third-order Differential Operator with Large Coefficients

Published online by Cambridge University Press:  14 February 2012

K. Unsworth
K. Unsworth
Affiliation:
Department of Aeronautics, Imperial College of Science and Technology, London.
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Synopsis

This paper sets out to study the spectrum of self-adjoint extensions of the minimal operator associated with the third-order formally symmetric differential expression. The technique employed is the method of singular sequences. Sufficient conditions are established on the coefficients of the differential expression in order that the spectrum should cover the entire real axis. Particular cases in which the coefficients behave roughly as powers of x as the magnitude of x becomes large are then considered, and certain conclusions are drawn regarding the spectra under different restrictions on these powers of x.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 4 , 1975 , pp. 299 - 305
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

References to Literature

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