Weighted composition semigroups on Hardy spaces (Q1093876)

On the Hardy space \(H^ p({\mathbb{D}})\) semigroups of the form \(T(t)f:=\frac{w\cdot \phi_ t}{w}f\circ \phi_ t\) are studied for a flow \(\phi_ t: {\mathbb{D}}\to {\mathbb{D}}\) and a weight function \(w: {\mathbb{D}}\to {\mathbb{C}}\). Strong continuity of the semigroup, its generator and its point spectrum are identified.