Phragm\'en--Lindel\"of principles for generalized analytic functions on unbounded domains

TL;DR

This paper extends classical maximum principles and Hadamard's three-lines theorem to generalized analytic functions on unbounded domains, broadening the scope of these fundamental complex analysis tools.

Contribution

It introduces new versions of Phragmén–Lindelöf principles and a Hadamard three-lines theorem for generalized analytic functions on unbounded domains.

Findings

Established Phragmén–Lindelöf principles for generalized analytic functions.

Derived a Hadamard three-lines theorem for these functions.

Extended classical complex analysis results to broader function classes.

Abstract

We prove versions of the Phragm\'en--Lindel\"of strong maximum principle for generalized analytic functions defined on unbounded domains. A version of Hadamard's three-lines theorem is also derived.