Alexander Strohmaier (Leeds)
A generalisation of the field of meromorphic functions and its application to scattering theory
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)