Curvilinear Integral Theorems for Monogenic Functions in Commutative Associative Algebras

摘要

We consider an arbitrary finite-dimensional commutative associative algebra, , with unit, over the field of complex number with m idempotents. Let e (1) = 1,e (2),e (3) be elements of 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.