Generators of C0-semigroups of weighted composition operators

Spectral sets of generalized Hausdorff matrices on spaces of holomorphic functions onD

“…This is a necessary assumption for our purposes. Indeed, if (v t C ϕt ) is a C 0 -semigroup in any of the spaces considered in Section 1, then (v t ) is a differentiable semicocycle for (ϕ t ), see for instance [17,27,29].…”

“…Unfortunately, (SCo3) rules out any Banach space X of holomorphic functions for which the inclusions H ∞ (D) ⊆ X ⊆ B 1 (D) hold (where B 1 (D) denotes the Bloch space) since no weighted composition semigroup is strongly continuous (at 0) in such a space X, see [17,Th. 4.1].…”

“…where Φ is the generator of (ϕ t ) and g is the generator of (v t ), that is, [34,Th. 2] and [17,Th. 2.1].…”