A Phragmén-Lindelöf Principle for Slice Regular Functions

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The celebrated 100-year old Phragmen-Lindelof principle is a far reaching extension of the maximum modulus theorem for holomorphic functions of one complex variable. In some recent papers there has been a resurgence of interest in principles of this type for functions of a hypercomplex variable and for solutions of suitable partial differential equations. In the present article we obtain a Phragmen-Lindelof principle for slice regular functions, a class of quaternion-valued functions of a quaternionic variable which has been recently introduced.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Bulletin of the Belgian Mathematical Society, volume 18, number 4, in 2011 following peer review. This article may not exactly replicate the final published version.

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Belgian Mathematical Society