Footnote:
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Description:
In this note, an alternative approach to establish observability for semigroups based on their smoothing properties is presented. The results discussed here reproduce some of 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].