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

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    S. A. Plaksa & V. S. Shpakovskii

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  1. S. A. Plaksa
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  2. V. S. Shpakovskii
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 7, pp. 967–973, July, 2013.

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Plaksa, S.A., Shpakovskii, V.S. On the Logarithmic Residues of Monogenic functions in a Three-Dimensional Harmonic Algebra with Two-Dimensional Radical. Ukr Math J 65, 1079–1086 (2013). https://doi.org/10.1007/s11253-013-0843-1

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  • DOI: https://doi.org/10.1007/s11253-013-0843-1

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