Spectral theory of difference operators with almost constant coefficients

Autor(en): Behncke, H.
Nyamwala, F. Oluoch
Stichwörter: absolutely continuous spectrum; difference operators; eigenvalues; 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: 677
Seitenende: 695
Zusammenfassung: 
The spectrum of higher even order difference operators with almost constant coefficients is determined. With appropriate smoothness and decay conditions on the coefficients, we show that singular continuous spectrum is absent and that the absolutely continuous spectrum agrees with that of the constant coefficient limiting operator. For such operators, the absolutely continuous spectrum is determined uniquely by the range of the characteristic polynomial. This result extends a similar result for even order differential operators. The methods of proof are closely related likewise. Finally, some results on fourth order operators with unbounded coefficients are shown.
ISSN: 10236198
DOI: 10.1080/10236190903160681

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