Uncertainty principles with error term in Gelfand-Shilov spaces

TL;DR

This paper introduces a new method to establish observability for semigroups using their smoothing properties, simplifying previous proofs by removing technical assumptions through complex analytic techniques.

Contribution

It provides an alternative proof approach that eliminates several technical assumptions, enhancing the theoretical framework for observability in semigroups.

Findings

Simplified proof of observability using smoothing properties

Removal of technical assumptions in existing results

Application of complex analytic methods to semigroup analysis

Abstract

In this note, an alternative approach to establish observability for semigroups based on their smoothing properties is presented. The results discussed here are closely related to those recently obtained in [arXiv:2112.01788], but the current proof allows to get rid of several technical assumptions by following the standard complex analytic approach established by Kovrijkine combined with an idea from [arXiv:2201.02370].