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Proceedings of the London Mathematical Society Advance Access published online on March 27, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn002
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© 2008 London Mathematical Society

Eigenfunctions, deficiency indices and spectra of odd-order differential operators

Horst Behncke

Fachbereich Mathematik/Informatik
Universität Osnabrück
49069 Osnabrück
Germany

D. B. Hinton

Mathematics Department
University of Tennessee
Knoxville, TN 37996
USA

Received 24 April 2007. Revision received 27 November 2007.

In this paper we determine the asymptotics of the eigenfunctions of a rather general class of odd-order operators on the half line. The coefficients are assumed to satisfy conditions which combine smoothness and decay. The asymptotics of these eigenfunctions allow to compute the deficiency indices of the associated operators. The results are also extended to operators on R, and whenever possible the spectra of the self-adjoint extensions are determined. The form of the eigenfunctions excludes singular continuous spectrum in all cases.

2000 Mathematics Subject Classification 34B20, 34B27, 34L05, 47L05.


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