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Bernard, E.
Archiv der Mathematik, 08/2022, Letnik: 119, Številka: 2Journal Article
We study, on certain Banach spaces X , families of weighted composition operators. Notably, we show that if this family forms a strongly continuous semigroup, then its infinitesimal generator ( Γ , D ( Γ ) ) is given by Γ f = g f + G f ′ with D ( Γ ) = { f ∈ X | g f + G f ′ ∈ X } where g , G are holomorphic functions. Moreover, our second main result is to study the reciprocal implication. That is, if ( Γ , D ( Γ ) ) , defined as above, generates a strongly continuous semigroup, then this one is a family of weighted composition operators.
