Characterization theorems of Riley type for bicomplex holomorphic functions

Yutaka Matsui; Yuhei Sato

doi:10.4134/CKMS.c190323

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2020; 35(3): 825-841

Online first article March 10, 2020 Printed July 31, 2020

https://doi.org/10.4134/CKMS.c190323

Characterization theorems of Riley type for bicomplex holomorphic functions

Yutaka Matsui, Yuhei Sato

Kindai University; Kindai University

Abstract

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Abstract

We characterize bicomplex holomorphic functions from several estimates. Originally, Riley \cite{Riley} studied such problems in local case. In our study, we treat global estimates on various unbounded domains. In many cases, we can determine the explicit form of a function.

Keywords: Bicomplex analysis, hypercomplex analysis, Riley's value

MSC numbers: Primary 30G35, 32D20