# Zero-one laws for operator semigroups

#### Jonathan Partington, University of Leeds. Part of the analysis and applications seminar series.

The classical 0-1 law for one-parameter semigroups (T(t)) of operators (Hille, 1950) says that either the lim sup of the norm of T(t)-I (as t goes to 0) is at least 1, or it is 0, in which case the semigroup is just exp(At) for some bounded operator A.

Using techniques of complex analysis and Fourier-Borel transforms, we look at generalisations of this, including the 0-1/4 law, and obtain estimates for a functional calculus for unbounded operators. This is joint work with I. Chalendar (Paris) and J. Esterle (Bordeaux).

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