https://doi.org/10.36719/2663-4619/111/186-189
Sabina Bashirova
Academy of Public Administration under the President of the Republic of Azerbaijan
https://orcid.org/0009-0001-1964-7221
bashirova.sabina310889@gmail.com
Direct and Inverse Problems of Spectral Analysis For Differential Operators
Abstract
Spectral analysis for differential operators covers direct and inverse spectral problems. In the direct spectral problem, the spectrum and eigenfunctions of the operator are determined, while in the inverse spectral problem, the structure of the operator is reconstructed using the given spectral data. Sturm-Liouville operators play an important role in spectral analysis and their applications are widespread in quantum mechanics, optics, and engineering. Methods such as Borg's theorem and the Gel'fand-Levitan-Marchenko integral equation are used to solve inverse spectral problems. In general, spectral analysis is of fundamental importance in the functional analysis, quantum physics, and applied mathematics fields of mathematics.
Keywords: differential operator, spectral analysis, direct spectral problem, inverse spectral problem, Sturm-Liouville operator, eigenvalues and eigenfunctions, spectral functions, Gel'fand-Levitan-Marchenko equation