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 Publication | Journal of Mathematical Analysis and Applications |
ISSN | 0022-247X |
Volume | 476Issue:2Pages:819-835 |
Abstract | In 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. |
Keyword | Fourier multipliers Fueter's theorem Monogenic functions Slice hyperholomorphic functions |
DOI | 10.1016/j.jmaa.2019.04.018 |
URL | View the original |
Language | 英語English |
Scopus ID | 2-s2.0-85064257690 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | University of Macau |
Corresponding Author | Qian，Tao |
Affiliation | 1.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 Affilication | University 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. |
Files in This Item: | ||||||
There are no files associated with this item. |
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment