A Cauchy integral formula in superspace
| Autor: | De Bie, H., Sommen, F. |
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| Rok vydání: | 2009 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/blms/bdp045 |
| Popis: | In previous work the framework for a hypercomplex function theory in superspace was established and amply investigated. In this paper a Cauchy integral formula is obtained in this new framework by exploiting techniques from orthogonal Clifford analysis. After introducing Clifford algebra valued surface- and volume-elements first a purely fermionic Cauchy formula is proven. Combining this formula with the already well-known bosonic Cauchy formula yields the general case. Here the integration over the boundary of a supermanifold is an integration over as well the even as the odd boundary (in a formal way). Finally, some additional results such as a Cauchy-Pompeiu formula and a representation formula for monogenic functions are proven. Comment: 14 pages, accepted for publication in the Bulletin of the LMS |
| Databáze: | arXiv |
| Externí odkaz: |
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