English

Curvilinear integral theorems for monogenic functions in commutative associative algebras

Complex Variables 2015-03-12 v1

Abstract

We consider an arbitrary finite-dimensional commutative associative algebra, Anm\mathbb{A}_n^m, with unit over the field of complex number with mm idempotents. Let e1=1,e2,e3e_1=1,e_2,e_3 be elements of Anm\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 xe1+ye2+ze3xe_1+ye_2+ze_3, where x,y,zx,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.

Keywords

Cite

@article{arxiv.1503.03464,
  title  = {Curvilinear integral theorems for monogenic functions in commutative associative algebras},
  author = {Vitalii Shpakivskyi},
  journal= {arXiv preprint arXiv:1503.03464},
  year   = {2015}
}