Mel'nichenko I. P.
Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1284-1290
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.
Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 228–243
We obtain new representations of the potential and flow function of three-dimensional potential solenoidal fields with axial symmetry, study principal algebraic analytic properties of monogenic functions of vector variables with values in an infinite-dimensional Banach algebra of even Fourier series, and establish the relationship between these functions and the axially symmetric potential or the Stokes flow function. The developed approach to the description of the indicated fields is an analog of the method of analytic functions in the complex plane used for the description of two-dimensional potential fields.
Ukr. Mat. Zh. - 1988. - 40, № 2. - pp. 229-231
Ukr. Mat. Zh. - 1986. - 38, № 2. - pp. 252–254