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Eigenfunctions, deficiency indices and spectra of odd‐order differential operators
Author(s) -
Behncke Horst,
Hinton D. B.
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdn002
Subject(s) - mathematics , eigenfunction , order (exchange) , spectral line , differential (mechanical device) , differential operator , pure mathematics , mathematical analysis , eigenvalues and eigenvectors , physics , quantum mechanics , thermodynamics , finance , economics
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.