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Differential forms and Clifford analysis

Irene Sabadini and Franciscus Sommen UGent (2016) Modern trends in hypercomplex analysis. In Trends in Mathematics p.247-264
abstract
In this paper we use a calculus of differential forms which is defi ned using an axiomatic approach. We then defi ne integration of differential forms over chains in a new way and we present a short proof of Stokes' formula using distributional techniques. We also consider differential forms in Clifford analysis, vector differentials and their powers. This framework enables an easy proof for a Cauchy's formula on a k-surface. Finally, we discuss how to compute winding numbers in terms of the monogenic Cauchy kernel and the vector differentials with a new approach which does not involve cohomology of differential forms.
Please use this url to cite or link to this publication:
author
organization
year
type
conference (other)
publication status
published
subject
keyword
Differential forms, Clifford algebras, monogenic functions, winding numbers
in
Modern trends in hypercomplex analysis
editor
Swanhild Bernstein, Uwe Kähler, Irene Sabadini and Franciscus Sommen UGent
series title
Trends in Mathematics
pages
247 - 264
publisher
Birkhäuser Basel
conference name
10th ISAAC Congress
conference location
Macau
conference start
2015-08-03
conference end
2015-08-08
ISSN
2297-0215
ISBN
978-3-319-42528-3
978-3-319-42529-0
DOI
10.1007/978-3-319-42529-0
language
English
UGent publication?
yes
classification
C1
copyright statement
I have transferred the copyright for this publication to the publisher
id
8502201
handle
http://hdl.handle.net/1854/LU-8502201
date created
2017-01-16 10:52:59
date last changed
2017-01-18 14:01:19
@inproceedings{8502201,
  abstract     = {In this paper we use a calculus of differential forms which is defi\unmatched{000c}ned using an axiomatic approach. We then defi\unmatched{000c}ne integration of differential forms over chains in a new way and we present a short proof of Stokes' formula using distributional techniques. We also consider differential forms in Clifford analysis, vector differentials and their powers.
This framework enables an easy proof for a Cauchy's formula on a k-surface. Finally, we discuss how to compute winding numbers in terms of the monogenic Cauchy kernel and the vector differentials with a new approach which does not involve cohomology of differential forms.},
  author       = {Sabadini, Irene and Sommen, Franciscus},
  booktitle    = {Modern trends in hypercomplex analysis},
  editor       = {Bernstein, Swanhild and K{\"a}hler, Uwe and Sabadini, Irene and Sommen, Franciscus},
  isbn         = {978-3-319-42528-3},
  issn         = {2297-0215},
  keyword      = {Differential forms,Clifford algebras,monogenic functions,winding numbers},
  language     = {eng},
  location     = {Macau},
  pages        = {247--264},
  publisher    = {Birkh{\"a}user Basel},
  title        = {Differential forms and Clifford analysis},
  url          = {http://dx.doi.org/10.1007/978-3-319-42529-0},
  year         = {2016},
}

Chicago
Sabadini, Irene, and Franciscus Sommen. 2016. “Differential Forms and Clifford Analysis.” In Modern Trends in Hypercomplex Analysis, ed. Swanhild Bernstein, Uwe Kähler, Irene Sabadini, and Franciscus Sommen, 247–264. Birkhäuser Basel.
APA
Sabadini, Irene, & Sommen, F. (2016). Differential forms and Clifford analysis. In S. Bernstein, U. Kähler, I. Sabadini, & F. Sommen (Eds.), Modern trends in hypercomplex analysis (pp. 247–264). Presented at the 10th ISAAC Congress, Birkhäuser Basel.
Vancouver
1.
Sabadini I, Sommen F. Differential forms and Clifford analysis. In: Bernstein S, Kähler U, Sabadini I, Sommen F, editors. Modern trends in hypercomplex analysis. Birkhäuser Basel; 2016. p. 247–64.
MLA
Sabadini, Irene, and Franciscus Sommen. “Differential Forms and Clifford Analysis.” Modern Trends in Hypercomplex Analysis. Ed. Swanhild Bernstein et al. Birkhäuser Basel, 2016. 247–264. Print.