Differential forms and Clifford analysis
- Author
- Irene Sabadini and Franciscus Sommen (UGent)
- Organization
- Abstract
- In this paper we use a calculus of differential forms which is defined using an axiomatic approach. We then define 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 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8502201
- MLA
- Sabadini, Irene, and Franciscus Sommen. “Differential Forms and Clifford Analysis.” Modern Trends in Hypercomplex Analysis, edited by Swanhild Bernstein et al., Birkhäuser, 2016, pp. 247–64, doi:10.1007/978-3-319-42529-0_14.
- APA
- Sabadini, I., & 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). https://doi.org/10.1007/978-3-319-42529-0_14
- Chicago author-date
- Sabadini, Irene, and Franciscus Sommen. 2016. “Differential Forms and Clifford Analysis.” In Modern Trends in Hypercomplex Analysis, edited by Swanhild Bernstein, Uwe Kähler, Irene Sabadini, and Franciscus Sommen, 247–64. Cham: Birkhäuser. https://doi.org/10.1007/978-3-319-42529-0_14.
- Chicago author-date (all authors)
- Sabadini, Irene, and Franciscus Sommen. 2016. “Differential Forms and Clifford Analysis.” In Modern Trends in Hypercomplex Analysis, ed by. Swanhild Bernstein, Uwe Kähler, Irene Sabadini, and Franciscus Sommen, 247–264. Cham: Birkhäuser. doi:10.1007/978-3-319-42529-0_14.
- 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. Cham: Birkhäuser; 2016. p. 247–64.
- IEEE
- [1]I. Sabadini and F. Sommen, “Differential forms and Clifford analysis,” in Modern trends in hypercomplex analysis, Macau, PEOPLES R CHINA, 2016, pp. 247–264.
@inproceedings{8502201, abstract = {{In this paper we use a calculus of differential forms which is defined using an axiomatic approach. We then define 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 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 Kähler, Uwe and Sabadini, Irene and Sommen, Franciscus}}, isbn = {{9783319425283}}, issn = {{2297-0215}}, keywords = {{Differential forms,Clifford algebras,monogenic functions,winding numbers}}, language = {{eng}}, location = {{Macau, PEOPLES R CHINA}}, pages = {{247--264}}, publisher = {{Birkhäuser}}, title = {{Differential forms and Clifford analysis}}, url = {{http://doi.org/10.1007/978-3-319-42529-0_14}}, year = {{2016}}, }
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