Unique continuation properties for Schroedinger operators in Hilbert spaces

Abstract

Here, the Morgan type uncertainty principle and unique continuation properties of abstract Schredinger equations with time dependent potentials are obtained in Hilbert space valued function classes. The equations include linear operator in abstract Hilbert spaces H dependent on space variables. So, by selecting appropriate spaces H and operators, we derive unique continuation properties for numerous classes of Schr\"odinger type equations and its systems, which occur in a wide variety of physical systems.