Functional calculus for bisectorial operators and applications to linear and non-linear evolution equations
146 pages, year of publication: 2005
price: 40.50 €
The holomorphic functional calculus for sectorial unbounded operators
is an extension of the classical Dunford calculus for bounded operators.
The interest in this calculus is motivated by the Kato square root
problem and applications to the operator-sum method introduced by
DaPrato and Grisvard to treat evolution equations on a finite interval.
In this thesis we develop the holomorphic functional calculus for
multisectorial and asymptotically bisectorial operators. We obtain
versions of closed-sum theorems that allow to deduce maximal regularity
for first and second order Cauchy problems both on the line and for the
periodic problem. The results are then applied to prove existence and
uniqueness of non-linear evolution equations.