Gallaun, DennisDennisGallaunMeichsner, JanJanMeichsnerSeifert, ChristianChristianSeifert2023-04-242023-04-242023-08Evolution Equations and Control Theory 12 (4): 1102-1121 (2023-08)http://hdl.handle.net/11420/15220This paper generalizes the abstract method of proving an observ-ability estimate by combining an uncertainty principle and a dissipation es-timate. In these estimates we allow for a large class of growth/decay rates satisfying an integrability condition. In contrast to previous results, we use an iterative argument which enables us to give an asymptotically sharp estimate for the observation constant and which is explicit in the model parameters. We give two types of applications where the extension of the growth/decay rates naturally appear. By exploiting subordination techniques we show how the dissipation estimate of a semigroup transfers to subordinated semigroups. Furthermore, we apply our results to semigroups related to Lévy processes.en2163-24802023411021121Banach spaceC -semigroups 0Final state observability estimatefractional powersnull-controllabilityJournal Article10.3934/eect.2023002Other