Curvilinear integral theorems for monogenic functions in commutative associative algebras

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 $x{e}_1+y{e}_2+z{e}_3$, 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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• Integral theorems for monogenic functions in commutative algebras