UM
The inverse Fueter mapping theorem for axially monogenic functions of degree k
Dong,Baohua1; Kou,Kit Ian2; Qian,Tao3; Sabadini,Irene4
2019-08-15
Source PublicationJournal of Mathematical Analysis and Applications
ISSN0022-247X
Volume476Issue:2Pages:819-835
AbstractIn this paper we first prove an important formula for the fractional Laplacian, and then we use it to invert the Fueter mapping theorem for axially monogenic functions of degree k. In fact, we prove that for every axially monogenic function of degree k f(x)=[A(x ,|x_|)+[Formula presented]B(x ,|x_|)]P (x_),x∈R , there exists a holomorphic intrinsic function f in C such that f(x)=τ (f )(x):=(−Δ) (f→ (x)P (x_)), where n can be any positive integer, k can be any non-negative integer, f→ is the slice monogenic function induced by f , and P (x_) is an inner spherical monogenic polynomial of degree k. Using the maps τ , k=0,1,2,…, we obtain a decomposition of a monogenic function for any value of the dimension n.
KeywordFourier multipliers Fueter's theorem Monogenic functions Slice hyperholomorphic functions
DOI10.1016/j.jmaa.2019.04.018
URLView the original
Language英語English
Scopus ID2-s2.0-85064257690
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorQian,Tao
Affiliation1.Department of Mathematics,Nanjing University of Information Science and Technology,Nanjing,210044,China
2.Faculty of Science and Technology,University of Macau,China
3.Macau Institute of Systems Engineering,Macau University of Science and Technology,China
4.Politecnico di Milano,Dipartimento di Matematica,Milano,Via Bonardi, 9,20133,Italy
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Dong,Baohua,Kou,Kit Ian,Qian,Tao,et al. The inverse Fueter mapping theorem for axially monogenic functions of degree k[J]. Journal of Mathematical Analysis and Applications,2019,476(2):819-835.
APA Dong,Baohua,Kou,Kit Ian,Qian,Tao,&Sabadini,Irene.(2019).The inverse Fueter mapping theorem for axially monogenic functions of degree k.Journal of Mathematical Analysis and Applications,476(2),819-835.
MLA Dong,Baohua,et al."The inverse Fueter mapping theorem for axially monogenic functions of degree k".Journal of Mathematical Analysis and Applications 476.2(2019):819-835.
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