Observatorio de I+D+i UPM

Memorias de investigación
Communications at congresses:
Chain Sequences and Location of Continuous Spectrum in Self Adjoint Difference Operators.
Year:2007
Research Areas
  • Mathematics
Information
Abstract
A closed solution in product form for the self-adjoint second order difference equation, x(n+1) = bn()x(n)􀀀anx(n􀀀1), relates oscillation properties [1] of the solution with Chain Sequences [2]. The solution fx(n)g1n=n0 is non oscillatory if and only if the sequence f (n + 1) = an+1 bn()bn+1()g, n > n0, is a chain sequence. Here, the difference operator associated to the previous equation has  as principal parameter, an example is the energy in difference Schrödinger operators. Applying the previous result in case of linear dependency, conditions are obtained for the rank of values of  where the solution can generate continuous spectrum. The equations of Harper and Fibonacci illustrate the results with numerical examples. The achievement of similar conditions seems admissible in other cases of dependency.
International
Si
Congress
XII International Conference on Difference Equations and Applications
960
Place
Lisboa, Portugal
Reviewers
Si
ISBN/ISSN
XXXXXXXXXX
Start Date
23/07/2008
End Date
27/07/2007
From page
To page
Participants
  • Autor: Emilio Torrano Gimenez (UPM)
  • Autor: Jesus Carmelo Abderraman Marrero (UPM)
Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Polinomios Ortogonales y Geometría Fractal
  • Departamento: Matemática Aplicada (Facultad de Informática)
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