2019
Том 71
№ 9

All Issues

Shpakovskii V. S.

Articles: 3
Article (Ukrainian)

On one class of quaternionic mappings

Kuz’menko T. S., Shpakovskii V. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 117-130

We consider a new class of quaternionic mappings associated with spatial partial differential equations. We obtain a description of all mappings from this class by using four analytic functions of complex variable.

Article (Russian)

On the Logarithmic Residues of Monogenic functions in a Three-Dimensional Harmonic Algebra with Two-Dimensional Radical

Plaksa S. A., Shpakovskii V. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 967–973

For monogenic (continuous and Gâteaux-differentiable) functions taking values in a three-dimensional harmonic algebra with two-dimensional radical, we compute the logarithmic residue. It is shown that the logarithmic residue depends not only on the roots and singular points of a function but also on the points at which the function takes values in the radical of a harmonic algebra.

Article (Russian)

Constructive description of monogenic functions in a harmonic algebra of the third rank

Plaksa S. A., Shpakovskii V. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1078–1091

By using analytic functions of a complex variable, we give a constructive description of monogenic functions that take values in a commutative harmonic algebra of the third rank over the field of complex numbers. We establish an isomorphism between algebras of monogenic functions in the case of transition from one harmonic basis to another.