Admissibility theory in abstract Sobolev scales and transfer function growth at high frequencies
Journal: arXiv (Cornell University)
Year: 2024

For strongly continous semigroups on Hilbert spaces, we investigate admissibility properties of control and observation operators shifted along continuous scales of spaces built by means of either interpolation and extrapolation or functional calculus. Our results show equivalence of admissibility in, on the one hand, a fractional domain of the generator and, on the other hand, a (different, in general) quadratic interpolation space of the same "Sobolev order". Furthermore, such properties imply