The inverse Fueter mapping theorem in integral form using spherical monogenics
type: Item
instance of: scholarly article
title: The inverse Fueter mapping theorem in integral form using spherical monogenics
zbMATH Open document ID: 1341.30042
author: Fabrizio Colombo
author: Irene Sabadini
author: Frank Sommen
published in: Israel Journal of Mathematics
publication date: 2013-06-18T00:00:00Z
full work available at URL: https://biblio.ugent.be/publication/3223578
review text: The Fueter mapping theorem states that given a holomorphic function \(f\) of a paravector variable defined on an axially symmetric open set \(U \subset\mathbb R^{n+1}\), where \(n\) is a odd number, then, for \(\mathcal P_k(\underline{x})\) a homogeneous monogenic polynomial of degree \(k\) and \(\Delta_x\) the Laplace operator in dimension \(n+1\), the function \( \breve{f}(x)\mathcal P_k(\underline{x})\) given by \[ \Delta_x^{\frac{n-1}{2}}\left( f(x)\mathcal P_k(\underline{x}) \right) = \breve{f}(x)\mathcal P_k(\underline{x}) \] is a monogenic function on \(U\). In this paper an integral representation formula of \(f(x)\mathcal P_k(\underline{x})\) is determined in terms of \(\breve{f}(x)\mathcal P_k(\underline{x}),\) allowing a Fueter primitive to be obtained for any monogenic function on an axially symmetric open set.
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 6176555
zbMATH Keywords: axial monogenic function
zbMATH Keywords: Fueter mapping theorem
zbMATH Keywords: spherical monogenic polynomial
reviewed by: Regina C. Almeida
MaRDI profile type: Publication
OpenAlex ID: W2052281762
cites work: A Structure Formula for Slice Monogenic Functions and Some of its Consequences
cites work: The Cauchy formula with s-monogenic kernel and a functional calculus for noncommuting operators
cites work: Analysis of Dirac systems and computational algebra.
cites work: The Fueter mapping theorem in integral form and the ℱ-functional calculus
cites work: The inverse Fueter mapping theorem
cites work: Slice monogenic functions
cites work: An extension theorem for slice monogenic functions and some of its consequences
cites work: A new functional calculus for noncommuting operators
cites work: Duality theorems for slice hyperholomorphic functions
cites work: Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions
cites work: Axial monogenic functions from holomorphic functions
cites work: Q4003806
cites work: Die Funktionentheorie der Differentialgleichungen \(\Delta u=0\) und \(\Delta\Delta u=0\) mit vier reellen Variablen
cites work: Slice regular functions on real alternative algebras
cites work: Q3995205
cites work: Q4515165
cites work: Q3414551
cites work: Q5621565
cites work: Generalizations of Fueter's theorem
cites work: An alternative proof of Fueter's theorem
cites work: Fourier analysis on starlike Lipschitz surfaces
cites work: Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space
cites work: Q3252796
cites work: On a generalization of Fueter's theorem
cites work: Q3677976
DOI: 10.1007/S11856-012-0090-4
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description: scientific article; zbMATH DE number 6176555