The essential spectrum of the Neumann--Poincaré operator on a domain with corners

Karl-Mikael Perfekt, Mihai Putinar

Published 2016-01-13Version 1

Exploiting the homogeneous structure of a wedge in the complex plane, we compute the spectrum of the anti-linear Ahlfors--Beurling transform acting on the Bergman space of the wedge. A classical similarity equivalence between the Ahlfors--Beurling transform and the Neumann--Poincar\'e operator then characterizes the spectrum also of the latter on a wedge. A localization technique leads to a complete description of the essential spectrum of the Neumann--Poincar\'e operator on a planar domain with corners.