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Article

Bureš, J. ; Souček, V.
The Penrose transform and Clifford analysis. (English). In: Bureš, J. and Souček, V. (eds.): Proceedings of the Winter School "Geometry and Physics". Circolo Matematico di Palermo, Palermo, 1991. pp. [97]-104
MSC: 30G35, 32A25, 32L25, 35J05, 58A10, 58J60, 81R25 | MR 1151894 | Zbl 0753.58033
Summary:
[For the entire collection see Zbl 0742.00067.]\par The Penrose transform is always based on a diagram of homogeneous spaces. Here the case corresponding to the orthogonal group $SO(2n,C)$ is studied by means of Clifford analysis [see {\it F. Brackx, R. Delanghe} and {\it F. Sommen}: Clifford analysis (1982; Zbl 0529.30001)], and is presented a simple approach using the Dolbeault realization of the corresponding cohomology groups and a simple calculus with differential forms (the Cauchy integral formula for solutions of the Laplace equation and the Leray residue for closed differential forms).
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