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Let A be the generator of a C0-semigroup T on a Banach space of analytic functions on the open unit disc. If T consists of composition operators, then there exists a holomorphic function G: \(\mathbb{D}\) → ℂ such that Af = Gf′ with maximal domain. The aim of the paper is the study of the reciprocal implication.

Generators of semigroups on Banach spaces inducing holomorphic semiflows