Unique continuation of Schr\"odinger-type equations for

The purpose of this paper is to study the unique continuation property for a Schr\"odinger-type equation u = Vu on a domain in Cⁿ, where the solution u may be a scalar function, or a vector-valued function. While simple examples show that the unique continuation property fails in general if the potential V L^p, p2n for n 3, or when V L₋₎₂^2n for n = 2. Finally, we discuss the unique continuation property for some special cases where V L₋₎₂^2n, for instance, V is a constant multiple of 1|z|.