Duelli, Markus

Functional calculus for bisectorial operators and applications to linear and non-linear evolution Equations

The holomorphic functional calculus for sectorial unbounded operatorsis an extension of the classical Dunford calculus for bounded operators.The interest in this calculus is motivated by the Kato square rootproblem and applications to the operator-sum method introduced byDaPrato and Grisvard to treat evolution equations on a finite interval.In this thesis we develop the holomorphic functional calculus formultisectorial and asymptotically bisectorial operators. We obtainversions of closed-sum theorems that allow to deduce maximal regularityfor first and second order Cauchy problems both on the line and for theperiodic problem. The results are then applied to prove existence anduniqueness of non-linear evolution equations.