Differentiable functions of quaternion variables
By S. Ludkovsky, F. van Oystaeyen. 2002
62 citations recorded by the source corpus.
Abstract 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 quternion 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.
Subfields: Applied Mathematics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/165d5bc0933a36c441232c55ecec14a412bcee0f
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In Applied Mathematics
In Statistical and Nonlinear Physics
Citations in the corpus
- Differentiable functions of Cayley-Dickson numbers and line integration (2004, background): “27.05.2004 A bstract W einvestigatesuperdi erentiabilityoffunctionsde ned on regions ofthe realoctonion (Cayley) algebra and obtain a noncom m utative version ofthe Cauchy-Riem ann conditions.”