2020/11/30 by Aiad El Gourari, Gourari, Aiad El, Allal Ghanmi +3
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV
paper · pdf · doi:10.48550/arxiv.2012.00126
19 pages, Improved version
arxiv created 2022/03/12 · arxiv updated 2022/03/15
In this paper, we are concerned with the bicomplex analog of the well-known result asserting that real-valued harmonic functions, on simply connected domains, are the real parts of holomorphic functions. We show that this assertion, word for word, fails for bc-harmonic functions and we provide a complete characterization of bc-harmonic functions that are the hyperbolic real parts of a specific kind of bc-holomorphic functions. Moreover, we extend the result to bicomplex polyharmonic functions, which implies the introduction of specific classes of bc-polyholomorphic functions.