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Hypermonogenic solutions and plane waves of the Dirac operator in R-p x R-q

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Abstract
In this paper we first define hypermonogenic solutions of the Dirac operator in R-p x R-q and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions.
Keywords
Hypermonogenic solution, Cauchy's formula, Plane wave

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Please use this url to cite or link to this publication:

Chicago
Guzmán Adán, Ali, Heikki Orelma, and Franciscus Sommen. 2019. “Hypermonogenic Solutions and Plane Waves of the Dirac Operator in R-p x R-q.” Applied Mathematics and Computation 346: 1–14.
APA
Guzmán Adán, A., Orelma, H., & Sommen, F. (2019). Hypermonogenic solutions and plane waves of the Dirac operator in R-p x R-q. APPLIED MATHEMATICS AND COMPUTATION, 346, 1–14.
Vancouver
1.
Guzmán Adán A, Orelma H, Sommen F. Hypermonogenic solutions and plane waves of the Dirac operator in R-p x R-q. APPLIED MATHEMATICS AND COMPUTATION. 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA: Elsevier; 2019;346:1–14.
MLA
Guzmán Adán, Ali, Heikki Orelma, and Franciscus Sommen. “Hypermonogenic Solutions and Plane Waves of the Dirac Operator in R-p x R-q.” APPLIED MATHEMATICS AND COMPUTATION 346 (2019): 1–14. Print.
@article{8604674,
  abstract     = {In this paper we first define hypermonogenic solutions of the Dirac operator in R-p x R-q and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions.},
  author       = {Guzm{\'a}n Ad{\'a}n, Ali and Orelma, Heikki and Sommen, Franciscus},
  issn         = {0096-3003},
  journal      = {APPLIED MATHEMATICS AND COMPUTATION},
  language     = {eng},
  pages        = {1--14},
  publisher    = {Elsevier},
  title        = {Hypermonogenic solutions and plane waves of the Dirac operator in R-p x R-q},
  url          = {http://dx.doi.org/10.1016/j.amc.2018.09.058},
  volume       = {346},
  year         = {2019},
}

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