Nonlinear bang-bang eigenproblems and optimization of resonances in layered cavities (Q2399500)

In this paper, the authors investigate the optimization of quasi-normal-eigenvalues \(\omega\) associated with the equation \[ y'' =-(\omega^2)By \eqno{(\star)} \] of two-side open optical and mechanical resonators. The paper contributes to the development and analytic justification of a numerical method based on the bang-bang eigenproblem. Also, the authors show that the eigenvalues associated with the equation \((\star)\) are not necessarily resonances of minimal decay. They obtain a variational characterization of the part of the spectrum outside of the imaginary line. To better understand the paper, I advice readers to read the appendices first.