AG Lie-Gruppen: Jonas Schober, Universidad Nacional Autónoma de México: The Scattering Matrix and a Levinson Theorem for a Class of Matrix-Valued Discrete Schrödinger Operators

The Scattering Matrix and a Levinson Theorem for a Class of Matrix-Valued Discrete Schrödinger Operators – Vortragender: Jonas Schober, Universidad Nacional Autónoma de México – Einladender: K.-H. Neeb

Abstract: On the vector-valued l²-space over the
integers we consider a free Hamiltonian that is a variation of the discrete
Laplacian and study scattering theory for the perturbation of this operator by
a matrix-valued potential. We prove the existence of the Jost-solutions and use
them to construct the scattering matrix, whose dimension in our model depends
on the spectral parameter. The scattering matrix and its analytic properties
are then used to formulate a Levinson type Theorem.