Unique Continuation Inequalities for the Schr\"odinger equations associated with the Special Hermite operators

Abstract

We investigate unique continuation inequalities for solutions of the Schr\"odinger equations associated with special Hermite operators. Our main result establishes that if the solution remains small at two distinct time points outside sets of finite measure, then the solution also remains small throughout the entire space. We also explore analogous results for the Hermite-Schr\"odinger equations.