# Branching form of the resolvent at threshold for discrete Laplacians

Kenichi Ito
(Kobe University)
Mat/Fys-seminar
Torsdag, 18 august, 2016, at 15:15-16:00, in Aud. D3 (1531-215)
Abstrakt:
We compute an explicit expression of the resolvent around the threshold zero for an ultra-hyperbolic operator of signature $(p,q)$, which includes the Laplacian as a special case. In particular, we classify a branching form of the resolvent; The resolvent has a square-root singularity if $(p,q)$ is odd-even or even-odd, a logarithm singularity if $(p,q)$ is even-even, and a dilogarithm singularity if $(p,q)$ is odd-odd. We apply the same computation scheme to the discrete Laplacian around thresholds embedded in continuous spectrum as well as those at end points, and obtain similar results, presenting a practical procedure to expand the resolvent around these thresholds. This talk is based on a recent joint work with Arne Jensen (Aalborg University).
Kontaktperson: Søren Fournais