http://hdl.handle.net/20.500.12323/6832 Professor of Mathematics 2026-04-15T05:37:56Z http://hdl.handle.net/20.500.12323/7946 Title: The-Resolvent-of-Impulsive-Singular-HahnSturmLiouville-Operators Authors: Allahverdiev, Bilender P.; Tuna, Hüseyin; Isayev, Hamlet A. Abstract: In this study, the resolvent of the impulsive singular Hahn–Sturm– Liouville operator is considered. An integral representation for the resolvent of this operator is obtained. 2024-01-01T00:00:00Z http://hdl.handle.net/20.500.12323/7945 Title: Fractal Sturm–Liouville Theory Authors: Golmankhaneh, Alireza Khalili; Vidović, Zoran; Tuna, Hüseyin; Allahverdiev, Bilender P. Abstract: This paper provides a short summary of fractal calculus and its application to generalized Sturm–Liouville theory. It presents both the fractal homogeneous and nonhomogeneous Sturm–Liouville problems and explores the theory’s applications in optics. We include examples and graphs to illustrate the effect of fractal support on the solutions and propose new models for fractal structures. 2025-04-22T00:00:00Z http://hdl.handle.net/20.500.12323/7937 Title: Eigenfunction Expansions for Singular Impulsive Dynamic Dirac Systems Authors: Allahverdiev, Bilender P.; Tuna, Hüseyin; Isayev, Hamlet A. Abstract: In this article, a spectral function for the singular impulsive dynamic Dirac system is obtained. In terms of this function, the Parseval equality and expansion formula in eigenfunctions is given. 2025-02-18T00:00:00Z http://hdl.handle.net/20.500.12323/7936 Title: Non-self-adjoint singular matrix Sturm–Liouville operators with general boundary conditions Authors: Allahverdiev, Bilender P. Abstract: In the Hilbert space L 2 A (I; E) (I := [a, b), −∞ < a < b ≤ +∞, dim E = m < +∞, A > 0), the maximal dissipative singular matrix-valued Sturm–Liouville operators that the extensions of a minimal symmetric operator with maximal deficiency indices (2m, 2m) (in limit-circle case at singular endpoint b) are studied. The maximal dissipative operators with general (for example coupled or separated) boundary conditions are investigated. A self-adjoint dilation is constructed for dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and determine its characteristic function in terms of the scattering matrix of the dilation (or in terms of the Weyl function of self-adjoint operator). Moreover a theorem on completeness of the system of eigenvectors and associated vectors (or root vectors) of the dissipative operators proved. 2024-01-01T00:00:00Z