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Discrete Clifford analysis: a germ of function theory

Fred Brackx UGent, Hennie De Schepper UGent, Franciscus Sommen UGent and Liesbet Van de Voorde UGent (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:
author
organization
year
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
Irene Sabadini, Michael Shapiro and Franciscus Sommen 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
2009-10-28 16:18:26
@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 I. 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.