On the inversion of Fueter’s theorem

Status	已發表Published
	On the inversion of Fueter’s theorem
	Dong, B.; Kou, K. I.; Qian, T.; Sabadini, I.
	2016-10-01
Source Publication	Journal of Geometry and Physics
ISSN	0393-0440
Pages	102-116
Abstract	The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space Rn+1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in Rn+1, where n is a positive integer, we can find a slice hyperholomorphic function View the MathML source such that View the MathML source. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.
Keyword	Fueter theorem Fourier multipliers Slice hyperholomorphic functions Axially monogenic functions
Language	英語English
The Source to Article	PB_Publication
PUB ID	22927
Document Type	Journal article
Collection	University of Macau
Corresponding Author	Qian, T.
Recommended Citation GB/T 7714	Dong, B.,Kou, K. I.,Qian, T.,et al. On the inversion of Fueter’s theorem[J]. Journal of Geometry and Physics, 2016, 102-116.
APA	Dong, B.., Kou, K. I.., Qian, T.., & Sabadini, I. (2016). On the inversion of Fueter’s theorem. Journal of Geometry and Physics, 102-116.
MLA	Dong, B.,et al."On the inversion of Fueter’s theorem".Journal of Geometry and Physics (2016):102-116.

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