Spectral analysis of \(q\)-Sturm-Liouville problem with the spectral parameter in the boundary condition
Many studies have been conducted regarding the spectral analysis of the Sturm-Liouville and Schrödinger differential equations, as well as discrete equations, with the spectral parameter in the boundary conditions. With the recent interest in quantum calculus, a number of investigators analyzed many aspects of the \(q\)-difference equations, including properties of eigenvalues and eigenvectors. In the current work, the author investigates the \(q\)-Sturm-Liouville boundary value problem in an appropriate Hilbert space, with an emphasis on the dissipation at the right endpoint and with the spectral parameter at zero. The functional model of the dissipative operator is constructed, and the theorems of completeness of the system of eigenvalues and corresponding eigenvectors of the dissipative \(q\)-difference operator, are presented.
\(q\)-Sturm-Liouville boundary value problem
scientific article; zbMATH DE number 6102740
scientific article