$α$-admissibility of the right-shift semigroup on $L^2(mathbb{R} )$

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It is shown that the right shift semigroup on $L^2(\mathbb{R} +)$ does not satisfy the weighted Weiss conjecture for $\alpha \in (0,1)$. In other words, $\alpha$-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-admis

Author: Andrew Wynn

Source: https://archive.org/