Essentially isospectral transformations and their applications
Spectral Theory
2020-07-01 v2 Mathematical Physics
Classical Analysis and ODEs
Functional Analysis
math.MP
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.
Cite
@article{arxiv.1708.07497,
title = {Essentially isospectral transformations and their applications},
author = {Namig J. Guliyev},
journal= {arXiv preprint arXiv:1708.07497},
year = {2020}
}
Comments
27 pages, minor corrections, to appear in Annali di Matematica Pura ed Applicata