The College of Education for Pure Sciences, Department of Mathematics, organized a scientific lecture entitled "Sturm-Liouvel Operators." The lecture, presented by student Yasser Nasser Hassan, covered:

Some well-known concepts in functional analysis and spectral theory were discussed, along with an example of an eigenvalue problem.

Generalizations and results related to dynamic equations on time series, including the q-difference equation as a special case, were presented. Subsequently, the q-inverse of the Sturm-Liouvel equation was derived, and some spectral properties of a second-order q-difference operator corresponding to that equation were discussed.

The lecture consisted of two parts. In the first part, the impulsive q-difference operator was defined, and a theory concerning the eigenvalues ​​and spectral singularities of this operator was presented. In the second part, some special cases were examined where the impulsive condition at the point t = 1 exhibits certain symmetries.

Keywords: q-difference equation, impulsive q-difference operator, Jost solution, eigenvalue, spectral singularity, symmetry

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