2017
Том 69
№ 9

All Issues

Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation

Mel'nichenko I. P.

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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.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 9, pp 1551-1559.

Citation Example: Mel'nichenko I. P. Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation // Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1284-1290.

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