Alexander Strohmaier (Leeds)
A generalisation of the field of meromorphic functions and its application to scattering theory
Abstract:
The scattering matrix and the resolvent of Schrödinger operators with fast decaying potentials
are well known to be meromorphic operator valued functions of the spectral parameter defined on a suitable cover of the complex plane.
Poles of the resolvent are either eigenvalues or scattering resonances. If the dimension of space is even
the resolvent is defined on a logarithmic cover of the complex place with branching point at zero.
One can introduce a class of functions which makes it possible to analyse the behaviour of the scattering matrix and the resolvent
at the point 0 in a very simple and direct way. I will review some of the classical stationary scattering theory and will then explain some new results that follow
from the existence a more general field of functions that allows for poles at the logarithmic branching point.
(based on joint work with J. Müller)