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math.AP2024
Admissibility theory in abstract Sobolev scales and transfer function growth at high frequencies
Lassi Paunonen, David Seifert, Nicolas Vanspranghe
For strongly continous semigroups on Hilbert spaces, we investigate admissibility properties of control and observation operators shifted along continuous scales of spaces built by…
math.FA2024
A non-uniform Datko-Pazy theorem for bounded operator semigroups
Lassi Paunonen, David Seifert, Nicolas Vanspranghe
We present a non-uniform analogue of the classical Datko-Pazy theorem. Our main result shows that an integrability condition imposed on orbits originating in a fractional domain of…
math.AP2024
Weakly elliptic damping gives sharp decay
Lassi Paunonen, Nicolas Vanspranghe, Ruoyu P. T. Wang
We prove that weakly elliptic damping gives sharp energy decay for the abstract damped wave semigroup, where the damping is not in the functional calculus. In this case, there is n…