Alpha-admissibility of the right-shift semigroup on L2(R‎+‎)

It is shown that the right-shift semigroup on L 2 ( R + ) does not satisfy the weighted Weiss conjecture for α ∈ ( 0 , 1 ) . In other words, α -admissibility of scalar valued observation operators cannot always be characterised by a simple resolvent growth condition. This result is in contrast to the unweighted case, where 0 -admissibility can be characterised by a simple growth bound. The result is proved by providing a link between discrete and continuous α -admissibility and then translating a counterexample for the unilateral shift on H 2 ( D ) to continuous time systems.