### Discrete Clifford analysis: a germ of function theory

(2009) Trends in Mathematics. p.37-53- 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.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-681651

- author
- Brackx, Fred UGent, De Schepper, Hennie UGent, Sommen, Franciscus UGent and Van de Voorde, Liesbet
- organization
- year
- 2009
- type
- conference
- publication status
- published
- subject
- keyword
- Discrete Clifford analysis, discrete function theory, discrete Cauchy integral formula, DIFFERENCE POTENTIALS, DIRAC OPERATORS
- in
- Trends in Mathematics
- editor
- Sabadini, Irene, Shapiro, Michael and Sommen, Franciscus UGent
- issue title
- Hypercomplex Analysis
- pages
- 17 pages
- publisher
- Birkhäuser Verlag
- place of publication
- Cambridge, MA, USA
- conference name
- 6th Congress of the International Society for Analysis its Applications and Computation
- conference location
- Ankara, Turkey
- conference start
- 2007-08-13
- conference end
- 2007-08-18
- Web of Science type
- Proceedings Paper
- Web of Science id
- 000264751300003
- ISBN
- 978-3-7643-9892-7
- language
- English
- UGent publication?
- yes
- classification
- P1
- id
- 681651
- handle
- http://hdl.handle.net/1854/LU-681651
- date created
- 2009-06-07 09:06:16
- date last changed
- 2017-01-02 09:52:55

@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}, keyword = {Discrete Clifford analysis,discrete function theory,discrete Cauchy integral formula,DIFFERENCE POTENTIALS,DIRAC OPERATORS}, language = {eng}, location = {Ankara, Turkey}, pages = {37--53}, publisher = {Birkh{\"a}user Verlag}, title = {Discrete Clifford analysis: a germ of function theory}, year = {2009}, }

- Chicago
- 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. Irene Sabadini, Michael Shapiro, and Franciscus Sommen, 37–53. Cambridge, MA, USA: Birkhäuser Verlag. - APA
- Brackx, Fred, De Schepper, H., Sommen, F., & Van de Voorde, L. (2009). Discrete Clifford analysis: a germ of function theory. In Irene Sabadini, M. Shapiro, & F. Sommen (Eds.),
*Trends in Mathematics*(pp. 37–53). Presented at the 6th Congress of the International Society for Analysis its Applications and Computation, 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.
- MLA
- Brackx, Fred, Hennie De Schepper, Franciscus Sommen, et al. “Discrete Clifford Analysis: a Germ of Function Theory.”
*Trends in Mathematics*. Ed. Irene Sabadini, Michael Shapiro, & Franciscus Sommen. Cambridge, MA, USA: Birkhäuser Verlag, 2009. 37–53. Print.