Complex Scaling and other spectral deformation methods for resonances
(by Peter Hislop)
This talk will review the theory of resonances for Schrödinger operators
originating with the work of Aguilar, Balslev, Combes and Simon. Emphasis will be
placed on the various spectral deformation methods that allow one to construct the
continuation of the resolvent, necessary in order to define resonances. The relation of
resonances to the eigenvalue problem for nonselfadjoint operators will also be
presented. The discussion will include the more recent refinements of complex scaling
due to Helffer, Sjöstrand, and Zworski, and a brief description of their application to
refined estimates on resonances.