Singular linear q-Hamiltonian systems

Abstract

In this paper, a singular linear q-Hamiltonian system is considered. The Titchmarsh–Weyl theory for this problem is constructed. Firstly, we provide some necessary fundamental concepts of the q-calculus. Later, we studied Titchmarsh–Weyl functions M (λ) and circles CTW (a, λ) for this system. Circles CTW (a, λ) are proved to be nested. In the fourth part of the work, the number of square-integrable solutions of this system is studied. In the fifth part of the work, boundary conditions in the singular case are obtained. Finally, a self-adjoint operator is defined.