From: Brenda Sue Frazier (brenda@math.missouri.edu)
Date: Fri Oct 05 2007 - 14:09:00 CDT
Harmonic Analysis Seminar
Monday, October 8, 2007
4:20-5:10 PM, GCB 209
Speaker: Roland Schnaubelt, University of Karlsruhe, Germany
Title: Exponential dichotomies of operator semigroups on Banach spaces
Gearhart's theorem says that a strongly continuous operator semigroup
on a Hilbert space $X$ has an exponential dichotomy if (and only if)
the resolvent of its generator exists and is bounded along the imaginary
axis. This important result is wrong if $X$ is not a Hilbert space,
unfortunately. There are various extensions of Gearhart's theorem to
Banach spaces imposing stronger conditions on the resolvent (e.g., it
should be a Fourier multiplier instead of being bounded). We proceed in
a different way: Keeping the more convenient boundedness assumption, we
obtain an exponential dichotomy with an unbounded splitting projection
whose domain contains a domain of a fractional power of the generator.
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