A q-difference operator with discrete and simple spectrum - Voulov, H. D.; Bohner, M. J.; Bekker, M. B. (Methods of Functional Analysis and Topology, 2011)
We continue our study of a q-difference version of a second-order differential operator which depends on a real parameter. This version was introduced in our previous article. For values of the parameter for which the difference operator is self adjoint, we show that the spectrum of the operator is discrete and simple. When q approaches 1, the spectrum fills the whole positive or negative semiaxis.