The inverse resonance problem for $\Z_2$-symmetric analytic obstacles in the plane

TL;DR

This paper demonstrates that the resonance poles uniquely determine two-component mirror-symmetric analytic obstacles in the plane, using a duality formula and extending previous interior case results.

Contribution

It establishes the inverse resonance problem for symmetric obstacles in the plane, providing a new proof approach and including comprehensive exposition.

Findings

Resonance poles uniquely determine symmetric obstacles.

The proof adapts interior case methods to exterior obstacles.

A duality formula simplifies the inverse problem proof.

Abstract

We prove that a two-component mirror-symmetric analytic obstacle in the plane is determined by its resonance poles among such obstacles. The proof is essentially the same as in the interior case (part II of the series). A so-called interior/exterior duality formula is used to simplify the proof. A fair amount of exposition is included for the sake of completeness.