InvestigationofthespectrumandtheJost solutionsofdiscreteDiracsystemonthe wholeaxis
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Date
2014
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Abstract
Weconsidertheboundaryvalueproblem(BVP)forthediscreteDiracequations y(2) n+1 –y(2) n +pny(1) n =λy(1) n , y(1) n–1 –y(1) n +qny(2) n =λy(2) n , n∈Z ={0,±1,±2,...}; y(1) 0 =0,
where(pn)and(qn),n∈Z arerealsequences,and λ isaneigenparameter.Wefinda polynomialtypeJostsolutionofthisBVP.Thenweinvestigatetheanalytical propertiesandasymptoticbehavioroftheJostsolution.UsingtheWeylcompact perturbationtheorem,weprovethataself-adjointdiscreteDiracsystemhasa continuousspectrumfillingthesegment[–2,2].WealsoprovethattheDiracsystem hasafinitenumberofrealeigenvalues.