Unique continuation estimates for the Kolmogorov equation in the whole space

TL;DR

This paper establishes a pointwise observation estimate for the Kolmogorov equation in the entire space, leading to controllability results when the control region is sufficiently widespread.

Contribution

It introduces a novel observation estimate for the Kolmogorov equation in the whole space, enabling controllability with distributed control regions.

Findings

Observation estimate at one point in time for the Kolmogorov equation

Implication of observability and null controllability in the whole space

Control region can be spread out throughout the entire space

Abstract

We prove in this Note an observation estimate at one point in time for the Kolmogorov equation in the whole space. Such estimate implies the observability and the null controllability for the Kolmogorov equation with a control region which is sufficiently spread out throughout the whole space.