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G-monogenic mappings in a three-dimensional noncommutative algebra
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2021-07-06 , DOI: 10.1080/17476933.2021.1947257 Tetiana Kuzmenko 1 , Vitalii Shpakivskyi 2
中文翻译:
三维非交换代数中的 G-单基因映射
更新日期:2021-07-06
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2021-07-06 , DOI: 10.1080/17476933.2021.1947257 Tetiana Kuzmenko 1 , Vitalii Shpakivskyi 2
Affiliation
In this paper, we consider some three-dimensional noncommutative algebra over the field , which contains the algebra of bicomplex numbers as a subalgebra. Locally bounded and Gâteaux-differentiable mappings defined in the domains of the three-dimensional subspace of the algebra and taking values in the algebra are considered. Such mappings generalize holomorphic functions of bicomplex variable and mentioned mappings are described by means of three holomorphic functions of a complex variable.
中文翻译:
三维非交换代数中的 G-单基因映射
在本文中,我们考虑一些三维非交换代数在场上,其中包含双复数的代数作为子代数。在代数的三维子空间域中定义的局部有界和 Gâteaux 可微映射并在代数中取值被考虑。这种映射概括了双复变量的全纯函数,并且所提到的映射是通过一个复变量的三个全纯函数来描述的。