Spectral Asymptotics of the Cauchy Operator and its Product with Bergman’s Projection on a Doubly Connected Domain

We found the exact asymptotics of the singular numbers for the Cauchy transform and its product with Bergman’s projection over the space \(L^{2}(\Omega ),\) $L^2(\mathrm{\Omega }),$ where \(\Omega \) $\mathrm{\Omega }$ is a doubly-connected domain in the complex plane.