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An Analog of the Menchov–Trokhimchuk Theorem for Monogenic Functions in a Three-Dimensional Commutative Algebra

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Ukrainian Mathematical Journal Aims and scope

The aim of the present work is to weaken the conditions of monogeneity for functions taking values in a given three-dimensional commutative algebra over the field of complex numbers. The monogeneity of a function is understood as a combination of its continuity with the existence of Gâteaux derivative.

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Authors and Affiliations

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

    M. V. Tkachuk & S. A. Plaksa

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  1. M. V. Tkachuk
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  2. S. A. Plaksa
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Correspondence to M. V. Tkachuk.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 8, pp. 1120–1128, August, 2021. Ukrainian DOI: 10.37863/umzh.v73i8.6658.

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Tkachuk, M.V., Plaksa, S.A. An Analog of the Menchov–Trokhimchuk Theorem for Monogenic Functions in a Three-Dimensional Commutative Algebra. Ukr Math J 73, 1299–1308 (2022). https://doi.org/10.1007/s11253-022-01991-w

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  • DOI: https://doi.org/10.1007/s11253-022-01991-w

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