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Characterization of Log-convex decay in non-selfadjoint dynamics

Supported by the Danish Research Council, Natural Sciences grant no. 4181-00042

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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.

    Mathematics Subject Classification: Primary: 35E15; Secondary: 47D06.


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