A Phragmén - Lindelöf principle for slice regular functions

Abstract

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.

10 pages

References in corpus (2)

• Poles of regular quaternionic functions
• The zero sets of slice regular functions and the open mapping theorem

Cited by in corpus (1)

• Slice regular Besov spaces of hyperholomorphic functions and composition operators