Semigroup admissibility along abstract Sobolev scales is equivalent to polynomial resolvent growth, and this equivalence yields sharp wave transfer function bounds and energy decay rates for Neumann damping.
Compact embeddings of vector valued Sobolev and Besov spaces
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Admissibility theory in abstract Sobolev scales and transfer function growth at high frequencies
Semigroup admissibility along abstract Sobolev scales is equivalent to polynomial resolvent growth, and this equivalence yields sharp wave transfer function bounds and energy decay rates for Neumann damping.