2015/03/24 by Vitalii Shpakivskyi, V. S. Shpakivskyi, Shpakivskyi, V. S. · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Complex Variables (math.CV) #FOS: Mathematics #math.CV
paper · pdf · doi:10.48550/arxiv.1503.07134
arXiv admin note: substantial text overlap with arXiv:1411.4643
arxiv created 2015/03/24 · openalex publication_date 2015/03/24 · arxiv updated 2015/03/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 obtain a constructive description of all mentioned functions by means of holomorphic functions of complex variables. It follows from this description that monogenic functions have Gateaux derivatives of all orders. The present article is generalized of the author's paper [1], where mentioned results are obtained for k=3.