Article ID Journal Published Year Pages File Type
1894203 Journal of Geometry and Physics 2010 18 Pages PDF
Abstract

By using complex geometric method associated to the Penrose transformation, we give a complete derivation of an exact sequence over C4nC4n, whose associated differential complex over HnHn is the kk-Cauchy–Fueter complex with the first operator D0(k) annihilating kk-regular functions. D0(1) is the usual Cauchy–Fueter operator and 11-regular functions are quaternionic regular functions. We also show that the kk-Cauchy–Fueter complex is elliptic. By using the fundamental solutions to the Laplacian operators of 44-order associated to the kk-Cauchy–Fueter complex, we can establish the corresponding Bochner–Martinelli integral representation formula, solve the non-homogeneous kk-Cauchy–Fueter equations and prove the Hartogs extension phenomenon for kk-regular functions in any bounded domain.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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