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Boundary value problems on fractal hypersurfaces for the quaternionic hermitian system in R-4n

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Abstract
In this paper we formulate and study Dirichlet and jump problems on fractal hypersurfaces in R4n for quaternionic Hermitian monogenic functions, using a circulant matrix approach. To this end we introduce the matrix Cauchy and Hilbert transforms on the fractal boundary of a bounded domain and prove a matricial Cauchy formula.
Keywords
Quaternionic Hermitian Clifford analysis, Boundary value problems, Fractal surfaces, CLIFFORD ANALYSIS

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MLA
Abreu-Blaya, Ricardo, et al. “Boundary Value Problems on Fractal Hypersurfaces for the Quaternionic Hermitian System in R-4n.” COMPLEX ANALYSIS AND OPERATOR THEORY, vol. 9, no. 5, 2015, pp. 957–73, doi:10.1007/s11785-014-0370-6.
APA
Abreu-Blaya, R., Bory-Reyes, J., Brackx, F., De Schepper, H., Moreno-Garcia, T., & Sommen, F. (2015). Boundary value problems on fractal hypersurfaces for the quaternionic hermitian system in R-4n. COMPLEX ANALYSIS AND OPERATOR THEORY, 9(5), 957–973. https://doi.org/10.1007/s11785-014-0370-6
Chicago author-date
Abreu-Blaya, Ricardo, Juan Bory-Reyes, Fred Brackx, Hennie De Schepper, Tania Moreno-Garcia, and Franciscus Sommen. 2015. “Boundary Value Problems on Fractal Hypersurfaces for the Quaternionic Hermitian System in R-4n.” COMPLEX ANALYSIS AND OPERATOR THEORY 9 (5): 957–73. https://doi.org/10.1007/s11785-014-0370-6.
Chicago author-date (all authors)
Abreu-Blaya, Ricardo, Juan Bory-Reyes, Fred Brackx, Hennie De Schepper, Tania Moreno-Garcia, and Franciscus Sommen. 2015. “Boundary Value Problems on Fractal Hypersurfaces for the Quaternionic Hermitian System in R-4n.” COMPLEX ANALYSIS AND OPERATOR THEORY 9 (5): 957–973. doi:10.1007/s11785-014-0370-6.
Vancouver
1.
Abreu-Blaya R, Bory-Reyes J, Brackx F, De Schepper H, Moreno-Garcia T, Sommen F. Boundary value problems on fractal hypersurfaces for the quaternionic hermitian system in R-4n. COMPLEX ANALYSIS AND OPERATOR THEORY. 2015;9(5):957–73.
IEEE
[1]
R. Abreu-Blaya, J. Bory-Reyes, F. Brackx, H. De Schepper, T. Moreno-Garcia, and F. Sommen, “Boundary value problems on fractal hypersurfaces for the quaternionic hermitian system in R-4n,” COMPLEX ANALYSIS AND OPERATOR THEORY, vol. 9, no. 5, pp. 957–973, 2015.
@article{5960894,
  abstract     = {{In this paper we formulate and study Dirichlet and jump problems on fractal hypersurfaces in R4n for quaternionic Hermitian monogenic functions, using a circulant matrix approach. To this end we introduce the matrix Cauchy and Hilbert transforms on the fractal boundary of a bounded domain and prove a matricial Cauchy formula.}},
  author       = {{Abreu-Blaya, Ricardo and Bory-Reyes, Juan and Brackx, Fred and De Schepper, Hennie and Moreno-Garcia, Tania and Sommen, Franciscus}},
  issn         = {{1661-8254}},
  journal      = {{COMPLEX ANALYSIS AND OPERATOR THEORY}},
  keywords     = {{Quaternionic Hermitian Clifford analysis,Boundary value problems,Fractal surfaces,CLIFFORD ANALYSIS}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{957--973}},
  title        = {{Boundary value problems on fractal hypersurfaces for the quaternionic hermitian system in R-4n}},
  url          = {{http://doi.org/10.1007/s11785-014-0370-6}},
  volume       = {{9}},
  year         = {{2015}},
}

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