Constructive description of monogenic functions in a finite-dimensional\n commutative associative algebra

2014/11/17 by Vitalii Shpakivskyi, Shpakivskyi, Vitalii
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1411.4643

openalex publication_date 2014/11/17 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Let mathbbA_n^m be an arbitrary n-dimensional commutative associative\nalgebra over the field of complex numbers with m idempotents. Let\ne₁=1,e₂,e₃ be elements of mathbbA_n^m which are linearly independent\nover the field of real numbers. We consider monogenic (i.e. continuous and\ndifferentiable in the sense of Gateaux) functions of the variable\nxe₁+ye₂+ze₃ where x,y,z are real, and obtain a constructive description\nof all mentioned functions by means of holomorphic functions of complex\nvariables. It follows from this description that monogenic functions have\nGateaux derivatives of all orders.\n

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