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doi: 10.3934/ipi.2021073
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## A new approach to the inverse discrete transmission eigenvalue problem

 1 Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, Samara 443086, Russia 2 Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia

*Corresponding author: Natalia P. Bondarenko

Received  June 2021 Revised  September 2021 Early access December 2021

Fund Project: The authors are supported by RFBR grants 20-31-70005, 19-01-00102

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.

Citation: Natalia P. Bondarenko, Vjacheslav A. Yurko. A new approach to the inverse discrete transmission eigenvalue problem. Inverse Problems & Imaging, doi: 10.3934/ipi.2021073
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