Herglotz–Riesz kernel

Summary

The Herglotz–Riesz kernel of a disc is the holomorphic function of $z$ whose real part is the Poisson kernel. Integrating it against the boundary values of a harmonic function $u$ gives a holomorphic function with real part $u$. It is the kernel in the Schwarz integral formula and in the Herglotz representation of holomorphic functions with positive real part.