Adıvar, Murat2023-06-162023-06-162010-11-301607-36061727-933Xhttps://doi.org/10.2989/16073606.2010.507323https://hdl.handle.net/20.500.14365/2449In this paper, a quadratic pencil of Schrodinger type difference operator L is taken under investigation to provide a general perspective for the spectral analysis of non-selfadjoint difference equations of second order. Introducing Jost-type solutions, structure and quantitative properties of the spectrum of L are investigated. Therefore, a discrete analog of the theory in [6] and [7] is developed. In addition, several analogies are established between difference and q-difference cases. Finally, the principal vectors of L are introduced to lay a groundwork for the spectral expansion.eninfo:eu-repo/semantics/openAccessEigenvalueJost solutionprincipal functionquadratic pencil of difference equationq-difference equationspectral analysisspectral singularitySingularitiesOperatorsArticle10.2989/16073606.2010.5073232-s2.0-79955369210