Abstract
Let F be an infinitesimal generator of a semigroup of holomorphic self-maps in a smooth strongly convex subdomain D of ℂ n . We prove that F ≡ 0 on D if F vanishes in angular sense at a boundary point up to third order.
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Acknowledgements
Finally, I wish to thank mainly Marco Abate, my research director, for guiding me in studying this topic and problem, and Filippo Bracci, Simeon Reich for their suggestions.