Differentiable functions of quaternion variables
Copyright policy )Differentiable functions of quaternion variables
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
- Physical Sciences Division Russian Federation
- Prokhorov General Physics Institute Russian Federation
- University of Antwerp Belgium
quaternionic analysis, Mathematics(all), 30C99 (Primary), 12E15, 30E20 (Secondary), Noncommutative algebraic geometry, Complex supergeometry, Mathematics - Complex Variables, Manifold, Quaternion function, superanalysis, Functions of hypercomplex variables and generalized variables, FOS: Mathematics, noncommutative geometry, Complex Variables (math.CV), Noncommutative geometry superanalysis, Mathematics
quaternionic analysis, Mathematics(all), 30C99 (Primary), 12E15, 30E20 (Secondary), Noncommutative algebraic geometry, Complex supergeometry, Mathematics - Complex Variables, Manifold, Quaternion function, superanalysis, Functions of hypercomplex variables and generalized variables, FOS: Mathematics, noncommutative geometry, Complex Variables (math.CV), Noncommutative geometry superanalysis, Mathematics
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