2008-2009

Tamara Kucherenko

**Monday, February 16
Millikan 213
(Pomona College), 3:00 PM**

**Title: **Absolute
functional calculus for sectorial operators

Abstract: We introduce absolute functional calculus for sectorial operators, which is stronger than H_\infty-calculus. Using this technique, we prove a theorem of Dore-Venni type for sums of closed operators. There, we are able to remove any assumptions such as R-boundedness or BIP on one of the operators given that the second operator has absolute calculus. Moreover, we show that any sectorial operator has absolute calculus on the real interpolation spaces between the domains of its fractional powers. As an application we obtain results regarding the well-posedness and existence of mild solutions to the Cauchy problem on Holder and Besov spaces.