LAUSR

Slice regular functions of several octonionic variables

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0 Published in 2020 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.6344

Abstract: A slice theory of several octonionic variables is introduced in the article as a generalization of the holomorphic theory of several complex variables. Our new trick is to focus our attentions on some subset of… read more here.

Keywords: functions several; several octonionic; regular functions; octonionic variables ... See more keywords

On the Structure of Octonion Regular Functions

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1 Published in 2019 at "Advances in Applied Clifford Algebras"

DOI: 10.1007/s00006-019-0983-y

Abstract: In this paper we study octonion regular functions and the structural differences between regular functions in octonion, quaternion, and Clifford analyses. read more here.

Keywords: octonion; octonion regular; regular functions; structure octonion ... See more keywords

Equivariant motivic integration and proof of the integral identity conjecture for regular functions

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0 Published in 2018 at "Mathematische Annalen"

DOI: 10.1007/s00208-019-01940-2

Abstract: We develop Denef–Loeser’s motivic integration to an equivariant version and use it to prove the full integral identity conjecture for regular functions. In comparison with Hartmann’s work, the equivariant Grothendieck ring defined in this article… read more here.

Keywords: conjecture regular; identity conjecture; conjecture; integral identity ... See more keywords

On Cauchy Integral Theorem for Quaternionic Slice Regular Functions

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1 Published in 2019 at "Complex Analysis and Operator Theory"

DOI: 10.1007/s11785-019-00913-2

Abstract: The aim of this work is to show that the operator G, which has been introduced in Colombo et al. (Trans Am Math Soc 365:303–318, 2013) and whose kernel kerG coincides with the set of… read more here.

Keywords: regular functions; cauchy integral; integral theorem; quaternionic slice ... See more keywords

Singularities of slice regular functions over real alternative ⁎-algebras

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0 Published in 2017 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2016.10.009

Abstract: Abstract The main goal of this work is classifying the singularities of slice regular functions over a real alternative ⁎-algebra A. This function theory has been introduced in 2011 as a higher-dimensional generalization of the… read more here.

Keywords: slice regular; slice; regular functions; real alternative ... See more keywords