On Penrose integral formula and series expansion of k-regular functions on the quaternionic space Hn

JOURNAL OF GEOMETRY AND PHYSICS

卷:64

Article

Kang, Qianqian¹  Wang, Wei² 

[1] Zhejiang Int Studies Univ, Coll Sci & Technol, Hangzhou 310012, Zhejiang, Peoples R China

[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

关键词: The k-Cauchy-Fueter operator;    Penrose integral formula;    Quaternionic k-regular functions;    Series expansion;    The sheaf of holomorphic functions homogeneous of degree m;    The Cech cohomology group;   

DOI  :  10.1016/j.geomphys.2012.11.002

来源: Elsevier

【 摘 要 】

The k-Cauchy-Fueter operator can be viewed as the restriction to the quaternionic space H-n of the holomorphic k-Cauchy-Fueter operator on C-4n. A generalized Penrose integral formula gives the solutions to the holomorphic k-Cauchy-Fueter equations, and conversely, any holomorphic solution to these equations is given by this integral formula. By restriction to the quaternionic space H-n subset of C-4n, we find all k-regular functions. The integral formula also gives the series expansion of a k-regular function by homogeneous k-regular polynomials. In particular, the result holds for left regular functions, which are exactly 1-regular. It is almost elementary to show the k-regularity of the function given by the integral formula or such series, but the proof of the inverse part that any k-regular function can be provided by the integral formula or such series involves some tools of sheaf theory. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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