Spektraltheorie gewöhnlicher linearer Differentialoperatoren vierter Ordnung

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Titel: Spektraltheorie gewöhnlicher linearer Differentialoperatoren vierter Ordnung
Sonstige Titel: Spectral Analysis of Fourth Order Differential Operators
Autor(en): Abels, Otto
Erstgutachter: Prof. Dr. H. Behncke
Zweitgutachter: Prof. Ph. D. D. Hinton
Zusammenfassung: In this thesis the spectral properties of differential operators generated by the formally self-adjoint differential expression Τy = w⁻₁[(ry″)″ - (py′)′ + qy] are investigated. The main tools to be used are the theory of asymptotic integration and the Titchmarsh--Weyl M-matrix. Subject to certain regularity conditions on the coefficients asymptotic integration leads to estimates for the eigenfunctions of the corresponding differential equation Τy = zy. According to the theory of asymptotic integration the regularity conditions combine smoothness with decay, i.e. admissible coefficients are (in an appropriate sense) either short range or slowly varying. Knowledge of the asymptotics (x → ∞) of the solutions will then be used to determine the deficiency index and to derive properties of the M-matrix which is closely related to the spectral measure of an associated self-adjoint realization Τ. Consequently we can compute the multiplicity of the spectrum, locate the absolutely continuous spectrum and give conditions for the singular continuous spectrum to be empty. This generalizes classical results on second order operators.
URL: https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2001072513
Schlagworte: fourth-order selfadjoint equation; asymptotic integration; Titchmarsh-Weyl M-Matrix; asymptotic formulae; solutions
Erscheinungsdatum: 25-Jul-2001
Enthalten in den Sammlungen:FB06 - E-Dissertationen

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