Exponential instability in the inverse scattering problem on the energy interval

TL;DR

This paper investigates the stability of the inverse scattering problem in three dimensions, establishing an exponential instability estimate that confirms the optimality of previous logarithmic stability results.

Contribution

It provides a new exponential instability estimate for the inverse scattering problem, demonstrating the limits of stability and confirming the optimality of prior logarithmic results.

Findings

Proves exponential instability estimate for inverse scattering

Shows optimality of Stefanov's logarithmic stability result

Highlights fundamental limits in stability for inverse scattering

Abstract

We consider the inverse scattering problem on the energy interval in three dimensions. We are focused on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows optimality of the logarithmic stability result of [Stefanov, 1990] (up to the value of the exponent).