Cayley-Dickson数的可微函数
Differentiable functions of Cayley-Dickson numbers
摘要：
研究了实八元数（Cayley）代数区域上函数的超可微性，得到了Cauchy-Riemann条件的一个非交换形式。然后，我们研究了柯西积分的非交换模拟以及八元数变量的函数是解析的准则。特别是，八元数指数和对数函数正在研究中。此外，还研究了有限维和无限维Cayley-Dickson代数（包含八元数代数作为真子代数）中变量的超可微函数。主要结果有Cauchy定理、Hurwitz定理、辐角原理、Mittag-Leffler定理、Rouche定理和Weierstrass定理的Cayley-Dickson代数类似。
英文摘要：
We investigate superdifferentiability of functions defined on regions of the real octonion (Cayley) algebra and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as criteria for functions of an octonion variable to be analytic. In particular, the octonion exponential and logarithmic functions are being investigated. Moreover, superdifferentiable functions of variables belonging to Cayley-Dickson algebras (containing the octonion algebra as the proper subalgebra) finite and infinite dimensional are investigated. Among main results there are the Cayley-Dickson algebras analogs of Cauchy's theorem, Hurwitz', argument principle, Mittag-Leffler's, Rouche's and Weierstrass' theorems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
