Spectral Properties of Potential Type Operators

Published in Pavillon André-Aisenstadt, room AA-5183, 2018

The Single Layer, Double Layer, and Steklov operators share many similarities. For example, the boundary plays a main role in all three. However, there are already striking differences with how their eigenvalues behave when we look at a circle. In this survey talk, we discuss each operator and it’s spectral properties. We start with relating the operators to each-other via decomposition and jump relations. Next, we discuss eigenvalue asymptotics, comparing with some of the few known explicitly computed examples, and state other known geometric facts.