Essentially isospectral transformations and their applications

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.

27 pages, minor corrections, to appear in Annali di Matematica Pura ed Applicata

References in corpus (2)

• Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions
• The inverse Sturm-Liouville problem with mixed boundary conditions

Cited by in corpus (7)

• Schrödinger operators with distributional potentials and boundary conditions dependent on the eigenvalue parameter
• Inverse square singularities and eigenparameter dependent boundary conditions are two sides of the same coin
• Harmonic Oscillator with a Step and its Isospectral Properties
• Spectral identities for Schrödinger operators
• Uniform stability for the inverse Sturm-Liouville problem with eigenparameter-dependent boundary conditions
• On selfadjoint extensions of symmetric operator with exit from space
• Direct and inverse spectral problems for the Schrodinger operator with double generalized Regge boundary conditions