A Logvinenko–Sereda theorem for vector-valued functions and application to control theory
Clemens Bombach
Technische Universität Chemnitz, Chemnitz, GermanyMartin Tautenhahn
Universität Leipzig, Leipzig, Germany

Abstract
We prove a Logvinenko–Sereda theorem for vector-valued functions. That is, for an arbitrary Banach space , all , all , all with , and all thick sets , we have
The constant is explicitly known independent of the geometric parameters of the thick set and the parameter . As an application, we study control theory for normally elliptic operators on Banach spaces whose coefficients of their symbol are given by bounded linear operators. This includes systems of coupled parabolic equations or problems depending on a parameter.
Cite this article
Clemens Bombach, Martin Tautenhahn, A Logvinenko–Sereda theorem for vector-valued functions and application to control theory. Z. Anal. Anwend. (2025), published online first
DOI 10.4171/ZAA/1794