Differentiable functions of quaternion variables
复变函数
2007-05-23 v1
摘要
We investigate differentiability of functions defined on regions of the real quaternion field 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 a quaternion variable to be analytic. In particular, the quaternionic exponential and logarithmic functions are being considered. Main results include quaternion versions of Hurwitz' theorem, Mittag-Leffler's theorem and Weierstrass theorem.
引用
@article{arxiv.math/0209166,
title = {Differentiable functions of quaternion variables},
author = {S. V. Ludkovsky and F. van Oystaeyen},
journal= {arXiv preprint arXiv:math/0209166},
year = {2007}
}
备注
48 pages, Latex