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 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.