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Two Spheres Uniquely Determine Infrabimonogenic Functions

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Abstract

In this paper we consider the problem of characterizing the sets of uniqueness for the solutions of the sandwich equation \(\partial _{\underline{x}}^3f\partial _{\underline{x}}\) = 0, where \(\partial _{\underline{x}}\) stands for the Dirac operator in \({{\mathbb {R}}}^m.\) These solutions are referred to as infrabimonogenic functions and can be viewed as a non-commutative version of biharmonic functions. Our main result states that a pair of distinct spheres is a set of uniqueness for infrabimonogenic functions in a convex domain of an odd-dimensional space.

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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Funding

Luis Miguel Martín Álvarez gratefully acknowledges the Financial support of the Postgraduate Study Fellowship of the Consejo Nacional de Ciencia y Tecnología (CONACYT) (Grant Number 962684)

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Chilpancingo de los Bravo, Mexico

    Luis Miguel Martín Alvarez, Martín Patricio Árciga Alejandre & Ricardo Abreu Blaya

  2. Facultad de Informática y Matemática, Universidad de Holguín, Holguín, Cuba

    Arsenio Moreno García

  3. Investigador Invitado, Universidad UTE, Quito, Ecuador

    Ricardo Abreu Blaya

Authors
  1. Luis Miguel Martín Alvarez
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  2. Arsenio Moreno García
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  3. Martín Patricio Árciga Alejandre
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  4. Ricardo Abreu Blaya
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All authors equally contributed to the results established in the paper.

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Correspondence to Ricardo Abreu Blaya.

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Alvarez, L.M.M., García, A.M., Alejandre, M.P.Á. et al. Two Spheres Uniquely Determine Infrabimonogenic Functions. Mediterr. J. Math. 20, 318 (2023). https://doi.org/10.1007/s00009-023-02523-x

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  • DOI: https://doi.org/10.1007/s00009-023-02523-x

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