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Menchov–Trokhimchuk Theorem Generalized for Monogenic Functions in a Three-Dimensional Algebra

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Analysis, Applications, and Computations (ISAAC 2021)

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

The aim of this work is to prove an analog of Menchov–Trokhimchuk theorem on weakening conditions of monogeneity for functions given in a concrete three-dimensional commutative algebra over the field of complex numbers. The property of monogeneity of a function is understood as a combination of its continuity with the existence of its Gâteaux derivative.

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Author information

Authors and Affiliations

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

    Maxim V. Tkachuk & Sergiy A. Plaksa

Authors
  1. Maxim V. Tkachuk
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  2. Sergiy A. Plaksa
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Universidade de Aveiro, Aveiro, Portugal

    Uwe Kähler

  2. Institut für Angewandte Analysis, TU Bergakademie Frieberg, Freiberg, Germany

    Michael Reissig

  3. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

  4. Department of Mathematics, Ghent University, Ghent, Belgium

    Jasson Vindas

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Tkachuk, M.V., Plaksa, S.A. (2023). Menchov–Trokhimchuk Theorem Generalized for Monogenic Functions in a Three-Dimensional Algebra. In: Kähler, U., Reissig, M., Sabadini, I., Vindas, J. (eds) Analysis, Applications, and Computations. ISAAC 2021. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-36375-7_25

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