The basic results of a new theory of regular functions of a quaternionic variable have been recently stated, following an idea of Cullen. In this paper we prove the minimum modulus principle and the open mapping theorem for regular functions. The proofs involve some peculiar geometric properties of such functions which are of independent interest.
@article{ASNSP_2009_5_8_4_805_0,
author = {Gentili, Graziano and Stoppato, Caterina},
title = {The open mapping theorem for regular quaternionic functions},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {805--815},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 8},
number = {4},
year = {2009},
mrnumber = {2647912},
zbl = {1201.30067},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2009_5_8_4_805_0/}
}
TY - JOUR AU - Gentili, Graziano AU - Stoppato, Caterina TI - The open mapping theorem for regular quaternionic functions JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 SP - 805 EP - 815 VL - 8 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2009_5_8_4_805_0/ LA - en ID - ASNSP_2009_5_8_4_805_0 ER -
%0 Journal Article %A Gentili, Graziano %A Stoppato, Caterina %T The open mapping theorem for regular quaternionic functions %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2009 %P 805-815 %V 8 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2009_5_8_4_805_0/ %G en %F ASNSP_2009_5_8_4_805_0
Gentili, Graziano; Stoppato, Caterina. The open mapping theorem for regular quaternionic functions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 805-815. http://www.numdam.org/item/ASNSP_2009_5_8_4_805_0/
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