Spectral theory of difference operators with almost constant coefficients II

Autor(en): Behncke, H.
Nyamwala, F. Oluoch
Stichwörter: absolutely continuous spectrum; difference operators; eigenvalues; LINEAR HAMILTONIAN-SYSTEMS; Mathematics; Mathematics, Applied; singular continuous spectrum; WEYL-TITCHMARSH THEORY
Erscheinungsdatum: 2011
Herausgeber: TAYLOR & FRANCIS LTD
Journal: JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
Volumen: 17
Ausgabe: 5
Startseite: 821
Seitenende: 829
Zusammenfassung: 
We show that the operators whose coefficients are approximately constant in a general sense have an absolutely continuous spectrum which is equal to that of the corresponding constant coefficient operator. For such operators, the absolutely continuous spectrum can be read off from the associated characteristic polynomial. This generalizes the classical results on second-order operators and extends those of higher order differential operators to the difference setting. Our approach relies on an analysis of the associated difference equation with the help of uniform asymptotic summation techniques.
ISSN: 10236198
DOI: 10.1080/10236190903413577

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