Boundary value problems on fractal hypersurfaces for the quaternionic hermitian system in R-4n
- Author
- Ricardo Abreu-Blaya, Juan Bory-Reyes, Fred Brackx (UGent) , Hennie De Schepper (UGent) , Tania Moreno-Garcia and Franciscus Sommen (UGent)
- Organization
- 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-5960894
- 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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