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arXiv · 1708.07497

Essentially isospectral transformations and their applications

Namig J. Guliyev
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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.

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BibTeXRIS

Namig J. Guliyev. 2017-08-24. Essentially isospectral transformations and their applications. https://doi.org/10.1007/s10231-019-00934-w

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