Depending on the behaviour of complex-valued electromagnetic potential in neighbourhood infinity, pseudomodes one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic approach which goes beyond standard semi-classical setting. Furthermore, this results substantial progress achieving optimal conditions and conclusions as well covering w...

Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. The can achieve arbitrarily high o...