Isaac Newton Institute for Mathematical Sciences

Some spectral problems for non-selfadjoint operators

21st June 2007

Author: Ian Wood (Aberystwyth, Wales)

Abstract

We consider abstract Dirichlet-to-Neumann operators (M-functions) for non-selfadjoint operators in an abstract setting. We prove that isolated eigenvalues of an operator correspond to poles of the associated M-function and show that second order elliptic PDEs in smooth domains satisfying fairly general boundary conditions fit into our framework.