A boundary rigidity problem of analytic function

Abstract

In 1994, Burns and Krantz proved that an analytic function on the unit disc approaching a ̄xed point at the boundary with certain rate must be identity. This is essentially a boundary rigidity condition. In this thesis, we present the phenomena on simply connected domain with nice boundary and in the case of non-tangential limit. We also investigate the boundary rigidity problem on the Blascke's product