Local solvability and stability of the generalized inverse Robin-Regge problem with complex coefficients

TL;DR

This paper establishes local solvability and stability for a complex coefficient inverse Robin-Regge problem, introducing a novel approach that reduces it to Sturm-Liouville potential recovery from Cauchy data.

Contribution

It provides the first proof of local solvability and stability for the generalized inverse Robin-Regge problem with complex coefficients, accounting for eigenvalue multiplicities.

Findings

Proved local solvability of the inverse problem.

Established stability estimates for the solution.

Reduced the inverse problem to Sturm-Liouville potential recovery.

Abstract

We prove local solvability and stability of the inverse Robin-Regge problem in the general case, taking eigenvalue multiplicities into account. We develop the new approach based on the reduction of this inverse problem to the recovery of the Sturm-Liouville potential from the Cauchy data.