Complex Analysis and Operator Theory

, Volume 10, Issue 1, pp 61–68 | Cite as

Phragmén–Lindelöf Principles for Generalized Analytic Functions on Unbounded Domains

Article

Abstract

We prove versions of the Phragmén–Lindelöf strong maximum principle for generalized analytic functions defined on unbounded domains. A version of Hadamard’s three-lines theorem is also derived.

Keywords

Phragmén–Lindelöf principle Generalized analytic function Pseudoanalytic function Three-lines theorem 

Mathematics Subject Classification

30G20 30C80 

Notes

Acknowledgments

The authors are grateful to Joseph Burrier for his assistance. They also thank the referee for some useful comments.

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.CNRS, UMR 5208, Institut Camille Jordan, Ecole Centrale de Lyon, INSA de Lyon, Université Lyon 1Université de LyonVilleurbanne CedexFrance
  2. 2.School of MathematicsUniversity of LeedsLeedsUK

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