In recent years there has been a surge of interest in polynomial decay properties
of solutions to various PDEs, most notably damped wave equations. Such polynomial
decay rates can be studied effectively using the framework of semigroup theory, by
exploiting a recently established link between polynomial decay properties of a
I will explain this link using the recently developed theory of operator-valued
This is joint work with Mark Veraar (Delft University of Technology), and with David Seifert (University of Oxford) and Reinhard Stahn (TU Dresden).