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, , with unit over the field of complex number with idempotents. Let 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 , where 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}
}