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Higher order Borel–Pompeiu representations in Clifford analysis

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Abstract
In this paper, we show that a higher order Borel–Pompeiu (Cauchy–Pompeiu) formula, associated with an arbitrary orthogonal basis (called structural set) of a Euclidean space, can be extended to the framework of generalized Clifford analysis. Furthermore, in lower dimensional cases, as well as for combinations of standard structural sets, explicit expressions of the kernel functions are derived.
Keywords
Borel–Pompeiu representation, subclass, structural set, Cauchy–Riemann operator, Clifford analysis, higher order Téodorescu transform, higher order Cauchy–type integral

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MLA
Bory Reyes, Juan et al. “Higher Order Borel–Pompeiu Representations in Clifford Analysis.” MATHEMATICAL METHODS IN THE APPLIED SCIENCES 39.16 (2016): 4787–4796. Print.
APA
Bory Reyes, J., De Schepper, H., Guzmán Adán, A., & Sommen, F. (2016). Higher order Borel–Pompeiu representations in Clifford analysis. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 39(16), 4787–4796. Presented at the 15th international conference on computational and mathematical methods in science and in general.
Chicago author-date
Bory Reyes, Juan, Hennie De Schepper, Ali Guzmán Adán, and Franciscus Sommen. 2016. “Higher Order Borel–Pompeiu Representations in Clifford Analysis.” Mathematical Methods in the Applied Sciences 39 (16): 4787–4796.
Chicago author-date (all authors)
Bory Reyes, Juan, Hennie De Schepper, Ali Guzmán Adán, and Franciscus Sommen. 2016. “Higher Order Borel–Pompeiu Representations in Clifford Analysis.” Mathematical Methods in the Applied Sciences 39 (16): 4787–4796.
Vancouver
1.
Bory Reyes J, De Schepper H, Guzmán Adán A, Sommen F. Higher order Borel–Pompeiu representations in Clifford analysis. MATHEMATICAL METHODS IN THE APPLIED SCIENCES. 111 RIVER ST, HOBOKEN 07030-5774, NJ, ENGLAND: WILEY-BLACKWELL; 2016;39(16):4787–96.
IEEE
[1]
J. Bory Reyes, H. De Schepper, A. Guzmán Adán, and F. Sommen, “Higher order Borel–Pompeiu representations in Clifford analysis,” MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol. 39, no. 16, pp. 4787–4796, 2016.
@article{8135233,
  abstract     = {In this paper, we show that a higher order Borel–Pompeiu (Cauchy–Pompeiu) formula, associated with an arbitrary orthogonal basis (called structural set) of a Euclidean space, can be extended to the framework of generalized Clifford analysis. Furthermore, in lower dimensional cases, as well as for combinations of standard structural sets, explicit expressions of the kernel functions are derived.},
  author       = {Bory Reyes, Juan and De Schepper, Hennie and Guzmán Adán, Ali and Sommen, Franciscus},
  issn         = {0170-4214},
  journal      = {MATHEMATICAL METHODS IN THE APPLIED SCIENCES},
  keywords     = {Borel–Pompeiu representation,subclass,structural set,Cauchy–Riemann operator,Clifford analysis,higher order Téodorescu transform,higher order Cauchy–type integral},
  language     = {eng},
  location     = {Cadiz, Spain},
  number       = {16},
  pages        = {4787--4796},
  publisher    = {WILEY-BLACKWELL},
  title        = {Higher order Borel–Pompeiu representations in Clifford analysis},
  url          = {http://dx.doi.org/10.1002/mma.3798},
  volume       = {39},
  year         = {2016},
}

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