Abstract
In commutative associative third-rank algebras with principal identity over a complex field, we select bases such that hypercomplex monogenic functions constructed in these bases have components satisfying the three-dimensional Laplace equation. The notion of monogeneity for these functions is similar to the notion of monogeneity in the complex plane.
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Mel'nichenko, I.P. Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation. Ukrainian Mathematical Journal 55, 1551–1559 (2003). https://doi.org/10.1023/B:UKMA.0000018016.99061.d7
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DOI: https://doi.org/10.1023/B:UKMA.0000018016.99061.d7