Namig J. Guliyev
Essentially isospectral transformations and their applications
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ABSTRACT.  We define and study the properties of Darboux-type transformations between Sturm Liouville problems with boundary conditions containing rational Herglotz Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary conditions). Using these transformations, we obtain various direct and inverse spectral results for these problems in a unified manner, such as asymptotics of eigenvalues and norming constants, oscillation of eigenfunctions, regularized trace formulas, and inverse uniqueness and existence theorems.