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Differential forms and Clifford analysis

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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.
Keywords
Differential forms, Clifford algebras, monogenic functions, winding numbers

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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.
@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},
}

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