Spectral theory and Galerkin approximations

Christian Engström
UMIT Research Lab
Department of Mathematics and Mathematical Statistics
Umeå University


Block operator matrices are used to study coupled systems of partial differential equations and problems with a nonlinear dependence of the spectral parameter. In this talk, I focus on Galerkin approximations of rational operator functions and block operator matrices. Simple examples illustrate the principle difficulties and show that a Galerkin approximation can produce results that are completely wrong.