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On the inversion of Fueter's theorem
Baohua Dong1; Kit Ian Kou1; Tao Qian1; Irene Sabadini2
Source PublicationJournal of Geometry and Physics

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 R, 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 R, where n is a positive integer, we can find a slice hyperholomorphic function f→ such that f=Δf→. 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.

KeywordAxially Monogenic Functions Fourier Multipliers Fueter Theorem Slice Hyperholomorphic Functions
URLView the original
Indexed BySCIE
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics ; Physics, Mathematical
WOS IDWOS:000383007000007
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Cited Times [WOS]:8   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Corresponding AuthorTao Qian
Affiliation1.Faculty of Science and Technology, University of Macau, Macau, China
2.Politecnico di Milano, Dipartimento di Matematica, Via Bonardi, 9, 20133 Milano, Italy
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Baohua Dong,Kit Ian Kou,Tao Qian,et al. On the inversion of Fueter's theorem[J]. Journal of Geometry and Physics,2016,108:102-116.
APA Baohua Dong,Kit Ian Kou,Tao Qian,&Irene Sabadini.(2016).On the inversion of Fueter's theorem.Journal of Geometry and Physics,108,102-116.
MLA Baohua Dong,et al."On the inversion of Fueter's theorem".Journal of Geometry and Physics 108(2016):102-116.
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