摘要
双曲复数形如a+bE,其中a、b是实数,E^2=1。本文通过在双曲复数中引进欧氏范数,使之成为巴拿赫空间,从而得到若干类似于复分析的结果,并且证明了解析的双曲复函数实现洛仑兹平面上的共形映射。
The hyperbolic complex numbers are of form a+bE, where a, b real, and E^2=1. The present paper generalizes some results of the real analysis to the case of hyperbolic complex by means of a suitable norm which makes the set of hyperbolic complex numbers to be a Banach space. It also shows that an analytic hyperbolic complex function gives rise to a conformal mapping in the Lorentzian plane.
关键词
双曲复数
巴拿赫空间
微分学
Hyperbolic complex number
Differential calculus
Banach space
