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Fundaments of quaternionic Clifford analysis II : splitting of equations

Fred Brackx UGent, Hennie De Schepper UGent, David Eelbode, Roman Lávička and Vladimir Souček (2017) COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. 62(5). p.616-641
abstract
Quaternionic Clifford analysis is a recent new branch of Clifford analysis, a higher dimensional function theory which refines harmonic analysis and generalizes to higher dimension the theory of holomorphic functions in the complex plane. So-called quaternionic monogenic functions satisfy a system of first-order linear differential equations expressed in terms of four interrelated Dirac operators. The conceptual significance of quaternionic Clifford analysis is unraveled by showing that quaternionic monogenicity can be characterized by means of generalized gradients in the sense of Stein and Weiss. At the same time, connections between quaternionic monogenic functions and other branches of Clifford analysis, viz Hermitian monogenic and standard or Euclidean monogenic functions are established as well.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Quaternionic Clifford analysis, Stein-Weiss gradients, splitting of equations
journal title
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
volume
62
issue
5
pages
616 - 641
publisher
TAYLOR & FRANCIS LTD
place of publication
2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND
Web of Science type
Article
Web of Science id
000395203300003
ISSN
1747-6933
1747-6941
DOI
10.1080/17476933.2016.1234463
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
8521917
handle
http://hdl.handle.net/1854/LU-8521917
date created
2017-06-01 07:15:03
date last changed
2017-06-07 08:44:13
@article{8521917,
  abstract     = {Quaternionic Clifford analysis is a recent new branch of Clifford analysis, a higher dimensional function theory which refines harmonic analysis and generalizes to higher dimension the theory of holomorphic functions in the complex plane. So-called quaternionic monogenic functions satisfy a system of first-order linear differential equations expressed in terms of four interrelated Dirac operators. The conceptual significance of quaternionic Clifford analysis is unraveled by showing that quaternionic monogenicity can be characterized by means of generalized gradients in the sense of Stein and Weiss. At the same time, connections between quaternionic monogenic functions and other branches of Clifford analysis, viz Hermitian monogenic and standard or Euclidean monogenic functions are established as well.},
  author       = {Brackx, Fred and De Schepper, Hennie and Eelbode, David and L{\'a}vi\v{c}ka, Roman and Sou\v{c}ek, Vladimir},
  issn         = {1747-6933},
  journal      = {COMPLEX VARIABLES AND ELLIPTIC EQUATIONS},
  keyword      = {Quaternionic Clifford analysis,Stein-Weiss gradients,splitting of equations},
  language     = {eng},
  number       = {5},
  pages        = {616--641},
  publisher    = {TAYLOR \& FRANCIS LTD},
  title        = {Fundaments of quaternionic Clifford analysis II : splitting of equations},
  url          = {http://dx.doi.org/10.1080/17476933.2016.1234463},
  volume       = {62},
  year         = {2017},
}

Chicago
Brackx, Fred, Hennie De Schepper, David Eelbode, Roman Lávička, and Vladimir Souček. 2017. “Fundaments of Quaternionic Clifford Analysis II : Splitting of Equations.” Complex Variables and Elliptic Equations 62 (5): 616–641.
APA
Brackx, Fred, De Schepper, H., Eelbode, D., Lávička, R., & Souček, V. (2017). Fundaments of quaternionic Clifford analysis II : splitting of equations. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 62(5), 616–641.
Vancouver
1.
Brackx F, De Schepper H, Eelbode D, Lávička R, Souček V. Fundaments of quaternionic Clifford analysis II : splitting of equations. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. 2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND: TAYLOR & FRANCIS LTD; 2017;62(5):616–41.
MLA
Brackx, Fred, Hennie De Schepper, David Eelbode, et al. “Fundaments of Quaternionic Clifford Analysis II : Splitting of Equations.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS 62.5 (2017): 616–641. Print.