A holomorphic function is reconstructed from its boundary values by the Cauchy kernel.Suggest a slogan
Let \(U\subseteq\CC\) be a bounded open set whose boundary \(\partial U\) consists of finitely many piecewise smooth closed curves, oriented positively with respect to \(U\), and let \(f\) be holomorphic on an open set containing \(\overline{U}\). Then for every \(p\in U\), \[ f(p)=\frac{1}{2\pi i}\int_{\partial U}\frac{f(z)}{z-p}\dz. \]