VAZN FUNKSIYA BILAN BERILGAN INTEGRAL GEOMETRIYA MASALASINI MODELLAShTIRISh - Djaykov, G.M.; Mamutova, G.Sh. (SCIENCE and SOCIETY, 2025)
The paper addresses the problem of function reconstruction based on integral equations. The approach relies on Fourier transforms and their inverses to recover the function from given data. It is emphasized that the analytical evaluation of the obtained solution is highly challenging due to the presence of poles in the kernel and oscillatory functions, which prevent the integral from being expressed in a closed form. Moreover, the strong sensitivity to noise in the data highlights the necessity of numerical methods. The article analyzes the efficiency of the applied methods and underlines the importance of regularization in the reconstruction process.
Keywords: integral equations; Fourier transform; inverse problem; regularization; function reconstruction