Singular linear q-Hamiltonian systems

Bilender Allahverdiev, Huseyin Tuna

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 \(M\left(  \lambda\right)\) and circles \(\mathcal{C}_{TW}\left(a,\lambda\right)\) for this system. Circles \(\mathcal{C}_{TW}\left(a,\lambda\right)\) 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.

Keywords


q-Hamiltonian system; singular point; Titchmarsh-Weyl theory.

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References


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DOI: http://dx.doi.org/10.17951/a.2024.78.1.1-15
Date of publication: 2024-07-29 22:47:27
Date of submission: 2024-07-11 13:52:49


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