This is the abstract of the paper
  "On the structure of the critical spectrum of strongly continuous semigroups"
by Simon Brendle and Rainer Nagel.

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Abstract: We show certain rotational symmetries of the recently introduced
critical spectrum of strongly continuous semigroups. Moreover, we study a
nonautonomous differential equation with infinite delay and show how the
critical spectrum can be used to characterize uniform exponential
stability of the solutions.