5 papers
Transmutation operators for the Sturm--Liouville equation in impedance form with an integrable potential
Briceyda B. Delgado, F. Ayça Çetinkaya
In this work, we study a family of transmutation operators for the Sturm--Liouville operator in impedance form with an integrable potential satisfying a smallness condition. Specif…
A Discrete Prüfer Transformation Approach to Sturm--Liouville Difference Equations and Eigenvalue Estimation
F. Ayça Çetinkaya, Kürşat Er, Hamza Menken
In this paper, we study regular second-order Sturm--Liouville difference equations using the discrete Prüfer transformation. By representing solutions in amplitude and phase coordi…
Inverse Quantum Potential Reconstruction via Generalized Bertlmann-Martin Inequalities
M. Gage Plott, F. Ayça Çetinkaya, Rick Mukherjee
Reconstructing a radial (1D) quantum potential, V(r), from a few bound-state energies is a long-standing inverse problem because limited spectral data must constrain an entire pote…
A Fractal Dirac Eigenvalue Problem: Spectral Properties and Numerical Examples
F. Ayça Çetinkaya, Gage Plott
In this paper, we study a Dirac boundary value problem where the operator is considered with a derivative of order , known as the -derivative. We prove some spect…
Inverse Scattering Problem for a Piecewise Continuous Sturm - Liouville Equation with Eigenparameter Dependence in the Boundary Conditon
Kh. R. Mamedov, Nida P. Kosar, F. Ayca Cetinkaya
In this study, the inverse problem of the scattering theory on the half line for a piecewise continuous Sturm-Liouville equation with boundary condition depending quadratic on the…