Some properties for quaternionic slice regular functions on domains without real points

DOI10.1080/17476933.2014.889691zbMath1318.30076arXiv1306.4295OpenAlexW3105292143MaRDI QIDQ4983297

Amedeo Altavilla

Publication date: 25 March 2015

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.4295

zbMATH Keywords

open mapping theoremslice regular functionsidentity principlefunction of a hypercomplex variableminimum modulus principle

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80)

Related Items (19)

Errata to: The algebra of slice functions ⋮ Slice regular functions as covering maps and global \(\star\)-roots ⋮ Slice-polynomial functions and twistor geometry of ruled surfaces in \(\mathbb {CP}^3\) ⋮ On some quaternionic generalized slice regular functions ⋮ s-regular functions which preserve a complex slice ⋮ On a class of orientation-preserving maps of \(\mathbb{R}^4\) ⋮ Twistor interpretation of slice regular functions ⋮ Quaternionic slice regularity beyond slice domains ⋮ \(\ast\)-logarithm for slice regular functions ⋮ On the real differential of a slice regular function ⋮ The algebra of slice functions ⋮ On slice polyanalytic functions of a quaternionic variable ⋮ Equivalence of slice semi-regular functions via Sylvester operators ⋮ Division algebras of slice functions ⋮ Holomorphicity of slice-regular functions ⋮ Geometric function theory over quaternionic slice domains ⋮ Spherical coefficients of slice regular functions ⋮ Log-biharmonicity and a Jensen formula in the space of quaternions ⋮ Transcendental operators acting on slice regular functions

Cites Work

• An extension theorem for slice monogenic functions and some of its consequences
• Slice regular functions on real alternative algebras
• Extension results for slice regular functions of a quaternionic variable
• Zeros of regular functions and polynomials of a quaternionic variable
• A new theory of regular functions of a quaternionic variable
• An integral theorem for analytic intrinsic functions on quaternions
• Regular Functions of a Quaternionic Variable
• The Zero Sets of Slice Regular Functions and the Open Mapping Theorem

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