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arXiv · 1503.03464

Curvilinear integral theorems for monogenic functions in commutative associative algebras

Vitalii Shpakivskyi
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Abstract

We consider an arbitrary finite-dimensional commutative associative algebra, $\mathbb{A}_n^m$, with unit over the field of complex number with $m$ idempotents. Let $e_1=1,e_2,e_3$ be elements of $\mathbb{A}_n^m$ which are linearly independent over the field of real numbers. We consider monogenic (i.e. continuous and differentiable in the sense of Gateaux) functions of the variable $xe_1+ye_2+ze_3$, where $x,y,z$ are real. For mentioned monogenic function we prove curvilinear analogues of the Cauchy integral theorem, the Morera theorem and the Cauchy integral formula.

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Vitalii Shpakivskyi. 2015-03-11. Curvilinear integral theorems for monogenic functions in commutative associative algebras. https://arxiv.org/abs/1503.03464

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