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