A new approach to the inverse discrete transmission eigenvalue problem

TL;DR

This paper introduces a novel method for solving the inverse discrete transmission eigenvalue problem, establishing well-posedness, uniqueness, and stability, with applications in acoustics.

Contribution

It develops a constructive procedure for the inverse problem, reducing it to a linear system with polynomial boundary conditions, and proves key theoretical properties.

Findings

Well-posed inverse problem formulation

Constructive solution procedure

Proof of uniqueness and stability

Abstract

A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove uniqueness of solution, global solvability, local solvability, and stability. Our approach is based on the reduction of the discrete transmission eigenvalue problem to a linear system with polynomials of the spectral parameter in the boundary condition.