A Phragmén - Lindelöf principle for slice regular functions
نویسندگان
چکیده
The celebrated 100-year old Phragmén-Lindelöf theorem, [15, 16], is a far reaching extension of the maximum modulus theorem for holomorphic functions that in its simplest form can be stated as follows: Theorem 1.1. Let Ω ⊂ C be a simply connected domain whose boundary contains the point at infinity. If f is a bounded holomorphic function on Ω and lim supz→z0 |f(z)| ≤ M at each finite boundary point z0, then |f(z)| ≤ M for all z ∈ Ω.
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