2015/03/24 by V. S. Shpakivskyi, Shpakivskyi, V. S.
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV
paper · pdf · doi:10.48550/arxiv.1503.07162
arXiv admin note: substantial text overlap with arXiv:1503.03464, arXiv:1503.07134
arxiv created 2015/03/24 · arxiv updated 2015/03/26
Let \mathbbAnm be an arbitrary n-dimensional commutative associative algebra over the field of complex numbers with m idempotents. Let e1=1,e2,…,ek with 2≤ k≤ 2n be elements of \mathbbAnm 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 ∑j=1k xj ej, where x1,x2,…,xk are real, and we prove curvilinear analogues of the Cauchy integral theorem, the Morera theorem and the Cauchy integral formula in k-dimensional (2≤ k≤ 2n) real subset of the algebra \mathbbAnm. The present article is generalized of the author's paper [1], where mentioned results are obtained for k=3.