Fundaments of quaternionic Clifford analysis II : splitting of equations
- Author
- Fred Brackx (UGent) , Hennie De Schepper (UGent) , David Eelbode, Roman Lávička and Vladimir Souček
- Organization
- 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.
- Keywords
- Quaternionic Clifford analysis, Stein-Weiss gradients, splitting of equations
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8521917
- MLA
- Brackx, Fred, et al. “Fundaments of Quaternionic Clifford Analysis II : Splitting of Equations.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, vol. 62, no. 5, TAYLOR & FRANCIS LTD, 2017, pp. 616–41, doi:10.1080/17476933.2016.1234463.
- APA
- Brackx, F., 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. https://doi.org/10.1080/17476933.2016.1234463
- Chicago author-date
- 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): 616–41. https://doi.org/10.1080/17476933.2016.1234463.
- Chicago author-date (all authors)
- 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. doi:10.1080/17476933.2016.1234463.
- 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. 2017;62(5):616–41.
- IEEE
- [1]F. Brackx, H. De Schepper, D. Eelbode, R. Lávička, and V. Souček, “Fundaments of quaternionic Clifford analysis II : splitting of equations,” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, vol. 62, no. 5, pp. 616–641, 2017.
@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 Lávička, Roman and Souček, Vladimir}},
issn = {{1747-6933}},
journal = {{COMPLEX VARIABLES AND ELLIPTIC EQUATIONS}},
keywords = {{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://doi.org/10.1080/17476933.2016.1234463}},
volume = {{62}},
year = {{2017}},
}
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