- Author
- Fred Brackx (UGent) , Hennie De Schepper (UGent) , Franciscus Sommen (UGent) and Liesbet Van de Voorde (UGent)
- Organization
- Abstract
- We develop a discrete version of Clifford analysis, i.e., a higher-dimensional discrete function theory in a Clifford algebra context. On the simplest of all graphs, the rectangular Z(m) grid, the concept of a discrete monogenic function is introduced. To this end new Clifford bases are considered, involving so-called forward and backward basis vectors, controlling the support of the involved operators. Following a proper definition of a discrete Dirac operator and of some topological concepts, function theoretic results amongst which Stokes' theorem, Cauchy's theorem and a Cauchy integral formula are established.
- Keywords
- Discrete Clifford analysis, discrete function theory, discrete Cauchy integral formula, DIFFERENCE POTENTIALS, DIRAC OPERATORS
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-681651
- MLA
- Brackx, Fred, et al. “Discrete Clifford Analysis : A Germ of Function Theory.” Trends in Mathematics, edited by Irene Sabadini et al., Birkhäuser Verlag, 2009, pp. 37–53.
- APA
- Brackx, F., De Schepper, H., Sommen, F., & Van de Voorde, L. (2009). Discrete Clifford analysis : a germ of function theory. In I. Sabadini, M. Shapiro, & F. Sommen (Eds.), Trends in Mathematics (pp. 37–53). Cambridge, MA, USA: Birkhäuser Verlag.
- Chicago author-date
- Brackx, Fred, Hennie De Schepper, Franciscus Sommen, and Liesbet Van de Voorde. 2009. “Discrete Clifford Analysis : A Germ of Function Theory.” In Trends in Mathematics, edited by Irene Sabadini, Michael Shapiro, and Franciscus Sommen, 37–53. Cambridge, MA, USA: Birkhäuser Verlag.
- Chicago author-date (all authors)
- Brackx, Fred, Hennie De Schepper, Franciscus Sommen, and Liesbet Van de Voorde. 2009. “Discrete Clifford Analysis : A Germ of Function Theory.” In Trends in Mathematics, ed by. Irene Sabadini, Michael Shapiro, and Franciscus Sommen, 37–53. Cambridge, MA, USA: Birkhäuser Verlag.
- Vancouver
- 1.Brackx F, De Schepper H, Sommen F, Van de Voorde L. Discrete Clifford analysis : a germ of function theory. In: Sabadini I, Shapiro M, Sommen F, editors. Trends in Mathematics. Cambridge, MA, USA: Birkhäuser Verlag; 2009. p. 37–53.
- IEEE
- [1]F. Brackx, H. De Schepper, F. Sommen, and L. Van de Voorde, “Discrete Clifford analysis : a germ of function theory,” in Trends in Mathematics, Ankara, Turkey, 2009, pp. 37–53.
@inproceedings{681651, abstract = {{We develop a discrete version of Clifford analysis, i.e., a higher-dimensional discrete function theory in a Clifford algebra context. On the simplest of all graphs, the rectangular Z(m) grid, the concept of a discrete monogenic function is introduced. To this end new Clifford bases are considered, involving so-called forward and backward basis vectors, controlling the support of the involved operators. Following a proper definition of a discrete Dirac operator and of some topological concepts, function theoretic results amongst which Stokes' theorem, Cauchy's theorem and a Cauchy integral formula are established.}}, author = {{Brackx, Fred and De Schepper, Hennie and Sommen, Franciscus and Van de Voorde, Liesbet}}, booktitle = {{Trends in Mathematics}}, editor = {{Sabadini, Irene and Shapiro, Michael and Sommen, Franciscus}}, isbn = {{978-3-7643-9892-7}}, keywords = {{Discrete Clifford analysis,discrete function theory,discrete Cauchy integral formula,DIFFERENCE POTENTIALS,DIRAC OPERATORS}}, language = {{eng}}, location = {{Ankara, Turkey}}, pages = {{37--53}}, publisher = {{Birkhäuser Verlag}}, title = {{Discrete Clifford analysis : a germ of function theory}}, year = {{2009}}, }