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Fundaments of quaternionic Clifford analysis II : splitting of equations

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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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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.
@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},
}

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