Functional calculus, variational methods and Liapunov's theorem

摘要

Given the generator −A of a holomorphic semigroup on a Hilbert space H, we show that A is associated with a closed form if and only if $A+win BIP(H)$ for some $winBbb{R}$ . Under this condition we also show that Liapunov's classical theorem is true, in the linear as well as the semilinear case.