On the Jost Solution and Its Properties of Quantum Difference Equations with Hyperbolic Eigenparameter
Ankara University, Faculty of Science, Department of Mathematics, 06100, Ankara, Turkey
This work is devoted to get Jost solution by the method of variation of parameters and properties of this Jost solution of a boundary value problem (BVP) depending on an hyperbolic eigenparameter. The results obtained are then used to find the Green function, resolvent and continuous spectrum of this BVP by using the methods of operator theory, methods of functional analysis and the general theory of difference equations. Moreover, using the Weyl compact perturbation theorem, we get that the operator L generated by the q -difference expression has continuous spectrum filling the segment [−2√q, 2√q].
© The Authors, published by EDP Sciences, 2016
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