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We obtain integral representations for the resolvent of ψ(A), where ψ is a holomorphic function mapping the right half-plane and the right half-axis into themselves, and A is a sectorial operator on a Banach space. As a corollary, for a wide class of functions ψ, we show that the operator −ψ(A) generates a sectorially bounded holomorphic C0-semigroup on a Banach space whenever −A does, and the sectorial...
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