2017
Том 69
№ 5

All Issues

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

Plaksa S. A., Shpakovskii V. S.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 7, pp 1079-1086.

Citation Example: Plaksa S. A., Shpakovskii V. S. 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.

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