The $L^p$-spectrum of the Dirac operator

We study the $L^p$-spectrum of the Dirac operator on complete manifolds. One of the main questions in this context is whether this spectrum is $p$-independent. As a first example where $p$-independence fails we compute explicitly the $L^p$-spectrum for the hyperbolic space and its product spaces. Moreover, we give general results on the Green functions and the symmetry of the $L^p$-spectrum of Dirac operator.

This is joint work with Bernd Ammann (Regensburg).