Inverse Problem for a Class of Dirac Operators with Spectral Parameter Contained in Boundary Conditions

TL;DR

This paper investigates an inverse spectral problem for a class of Dirac operators with discontinuous coefficients and eigenvalue-dependent boundary conditions, establishing eigenvalue asymptotics, completeness, expansion formulas, and uniqueness results.

Contribution

It introduces a novel inverse problem framework for Dirac operators with spectral parameters in boundary conditions, proving key properties and uniqueness theorems.

Findings

Eigenvalue asymptotic formulas derived

Completeness of eigenfunctions proved

Uniqueness of inverse problem established

Abstract

This paper is related to an inverse problem for a class of Dirac operators with discontinuous coefficient and eigenvalue parameter contained in boundary conditions. The asymptotic formula of eigenvalues of this problem is examined. The theorem on completeness of eigenfunctions is proved. The expansion formula with respect to eigenfunctions is obtained and Parseval equality is given. Weyl solution and Weyl function are constructed. Uniqueness theorem of the inverse problem respect to the Weyl function is proved.