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Holomorphicity of slice-regular functions. (arXiv:1807.05899v1 [math.CV])
来源于:arXiv
Slice-regular functions of a quaternionic variable have been studied
extensively in the last 12 years, resulting, in many ways, quite close to
classical holomorphic functions of a complex variable; indeed, there is a
correspondence between slice-regular functions and a certain family of
holomorphic maps from the complex plane to $\mathbb{C}^4$, as noted by Ghiloni
and Perotti. However, such a construction does not seem to offer any insight on
the behaviour of slice-regular functions, due to the lack of a connection
between the values of the holomorphic map and the values of the associated
sliceregular function. The aim of this work is to show that there is indeed a
(complex) geometric way to relate the values of this two functions, thus
relating more deeply the world of holomorphic functions with that of
slice-regular functions. 查看全文>>