Singularities of slice regular functions over real alternative \(^{\ast}\)-algebras

DOI10.1016/j.aim.2016.10.009zbMath1408.30045arXiv1606.03609OpenAlexW2434246344MaRDI QIDQ340438

Riccardo Ghiloni, Caterina Stoppato, Alessandro Perotti

Publication date: 14 November 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.03609

zbMATH Keywords

singularitiesquaternionsslice regular functionsalternative *-algebrasLaurent series and expansionspower series and expansionssemiregular functionsspherical series and expansions

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Alternative rings (17D05) Holomorphic functions of several complex variables (32A99)

Related Items (24)

Errata to: The algebra of slice functions ⋮ Slice-polynomial functions and twistor geometry of ruled surfaces in \(\mathbb {CP}^3\) ⋮ The Cauchy transform in the slice hyperholomorphic setting and related topics ⋮ Slice regular functions in several variables ⋮ On a class of orientation-preserving maps of \(\mathbb{R}^4\) ⋮ Slice conformality and Riemann manifolds on quaternions and octonions ⋮ Slice Fueter-regular functions ⋮ \(\ast\)-logarithm for slice regular functions ⋮ Slice Regularity and Harmonicity on Clifford Algebras ⋮ The algebra of slice functions ⋮ Equivalence of slice semi-regular functions via Sylvester operators ⋮ Division algebras of slice functions ⋮ Slice regular semigroups ⋮ Applications of the Sylvester operator in the space of slice semi-regular functions ⋮ On geometric aspects of quaternionic and octonionic slice regular functions ⋮ Implementing zonal harmonics with the Fueter principle ⋮ Geometric function theory over quaternionic slice domains ⋮ Growth theorems in slice analysis of several variables ⋮ Spherical coefficients of slice regular functions ⋮ The harmonicity of slice regular functions ⋮ Log-biharmonicity and a Jensen formula in the space of quaternions ⋮ Transcendental operators acting on slice regular functions ⋮ Slice regular functions and orthogonal complex structures over \(\mathbb{R}^8\) ⋮ Slice-by-slice and global smoothness of slice regular and polyanalytic functions

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