A paper by the research fellow at the department of Functional Analysis of the Institute of Mathematics and Mechanics, Namig Guliyev has been published in the journal “Annali di Matematica Pura ed Applicata” refereed by the international database “Clarivate Analytics” with a high impact-factor 1.268.

In the paper entitled “Essentially isospectral transformations and their applications” the author defines and studies the properties of Darboux-type transformations between Sturm–Liouville problems with boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter. Using these transformations, he then obtains various direct and inverse spectral results (asymptotics of eigenvalues and norming constants, oscillation of eigenfunctions, trace formulas, uniqueness and existence of the reconstruction by spectral data, various inverse problems by one spectrum) for problems with such boundary conditions.