Direct and inverse spectral problems for the Schrodinger operator with double generalized Regge boundary conditions

TL;DR

This paper investigates spectral problems for the Schrödinger operator with generalized boundary conditions, providing spectral properties and uniqueness results for inverse problems, including special cases like even potentials and two-spectra scenarios.

Contribution

It introduces new uniqueness theorems for inverse spectral problems with generalized Regge boundary conditions, extending previous results to broader boundary cases.

Findings

Spectral properties and eigenvalue asymptotics established.

Uniqueness theorems proved for inverse problems with various boundary conditions.

Results include special cases like even potentials and two-spectra inverse problems.

Abstract

In this paper, we study the direct and inverse spectral problems for the Schrodinger operator with two generalized Regge boundary conditions. For the direct problem, we give the properties of the spectrum, including the asymptotic distribution of the eigenvalues. For the inverse problems, we prove several uniqueness theorems, including the cases: even potential, two-spectra, as well as the general partial inverse problem.