Integral theorems for monogenic functions in an infinite-dimensional space with a commutative multiplication

Authors

  • Sergiy Anatoliyovych Plaksa Department of Complex Analysis and Potential Theory, Institute of Mathematics, National Academy of Sciences of Ukraine
  • Vitalii Stanislavovych Shpakivskyi Department of Complex Analysis and Potential Theory, Institute of Mathematics, National Academy of Sciences of Ukraine

DOI:

https://doi.org/10.26485/0459-6854/2018/68.2/2

Keywords:

Laplace equation, spatial potentials, harmonic algebra, topological vector space, differentiable in the sense of Gateaux function, monogenic function, Cauchy- Riemann conditions

Abstract

We consider monogenic functions taking values in a topological vector space being an expansion of a certain infinite-dimensional commutative Banach algebra associated with the three-dimensional Laplace equation. We establish also integral theorems for monogenic functions taking values in the mentioned algebra and the mentioned topological vector space.

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Published

2019-04-26

Issue

Vol. 68 No. 2 (2018)

Section

Articles