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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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Chicago
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.
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.
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.
MLA
Abreu-Blaya, Ricardo, Juan Bory-Reyes, Fred Brackx, et al. “Boundary Value Problems on Fractal Hypersurfaces for the Quaternionic Hermitian System in R-4n.” COMPLEX ANALYSIS AND OPERATOR THEORY 9.5 (2015): 957–973. Print.
@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},
  language     = {eng},
  number       = {5},
  pages        = {957--973},
  title        = {Boundary value problems on fractal hypersurfaces for the quaternionic hermitian system in R-4n},
  url          = {http://dx.doi.org/10.1007/s11785-014-0370-6},
  volume       = {9},
  year         = {2015},
}

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