Spectral inequalities, that is, bounding the L^2-norm of (a class of) functions with respect to its L^2-norm on a restriction to smaller set, is a key assignment in control theory. In this talk we will present such estimates for (linear combinations of) eigenfunctions of one-dimensional vector-valued self-adjoint operators where the restricted set satisfies a certain geometric condition. As an application, we will discuss the setting of the magnetic Laplacian on metric graphs. Joint work with Delio Mugnolo (FerUni Hagen) and Albrecht Seelmann (Technische Universität Dortmund)
