Differentiable functions of quaternion variables

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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.
48 pages, Latex

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Complex Variables, 30C99 (Primary), 12E15, 30E20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/64937

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0209166
 http://arxiv.org/abs/math/0209166

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arXiv