Akademik Məlumat İdarəetmə Sistemi
Ufa Mathematical Journal, vol.14, no.4, pp.127-140, 2022 (Scopus)
In this work, we study a Hahn–Hamiltonian system in the singular case. For this system, the Titchmarsh–Weyl theory is established. In this context, the first part provides a summary of the relevant literature and some necessary fundamental concepts of the Hahn calculus. To pass from the Hahn difference expression to operators, we define the Hilbert space L2ω,q,W((ω0,∞);C2n) in the second part of the work. The corresponding maximal operator Lmax are introduced. For the Hahn–Hamiltonian system, we proved Green formula. Then we introduce a regular self-adjoint Hahn–Hamiltonian system. In the third part of the work, we study Titchmarsh-Weyl functions M(λ) and circles C(a,λ) for this system. These circles proved to be embedded one to another. The number of squareintegrable solutions of the Hahn–Hamilton system is studied. In the fourth part of the work, we obtain boundary conditions in the singular case. Finally, we define a self-adjoint operator in the fifth part of the work.