Operators with Simple Characteristics: Calderón’s Theorems

Abstract

We study in this chapter the simplest form of A. Calderón’s theorems, providing unique continuation properties for operators with simple characteristics. We assume here that the operator under scope has real coefficients and that the characteristic roots are simple. We do not use a pseudo-differential factorization and we prove a Carleman estimate following a general method introduced by L. Hörmander. Although our main results are using pseudo-differential analysis, we provide as well a theorem for elliptic operators with simple characteristics using a local method involving differential quadratic forms.