Characterisation of log-convex decay in non-selfadjoint dynamics

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The short-time and global behavior are studied for an autonomous linear evolution equation, which is defined by a generator inducing a uniformly bounded holomorphic semigroup in a Hilbert space. A general necessary and sufficient condition is introduced under which the norm of the solution is shown to be a log-convex and strictly decreasing function of time, and differentiable also at the initial time with a derivative controlled by the lower bound of the generator, which moreover is shown to be positively accretive. Injectivity of holomorphic semigroups is the main technical tool.
Original languageEnglish
JournalElectronic Research Archive (ERA)
Pages (from-to)72-86
Number of pages15
Publication statusPublished - 2018


  • log-convex decay
  • non-selfadjoint
  • hyponormal
  • positively accretive operators
  • short-time behavior


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