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Characterization of Classes of Polynomial Functions

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Abstract

In this paper, some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization, we introduce a numerical quantity depending on the variety of the local polynomial only. Moreover, we show that the known characterization of polynomials among generalized polynomials can be simplified: a generalized polynomial is a polynomial if and only if its variety contains finitely many linearly independent additive functions.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Jaén, E.P.S. Linares, C/Alfonso X el Sabio, 28, 23700, Linares, Spain

    J. M. Almira

  2. Institute of Mathematics, University of Debrecen, Egyetem tér 1, Debrecen, 4032, Hungary

    L. Székelyhidi

  3. Department of Mathematics, University of Botswana, 4775 Notwane Rd., Gaborone, Botswana

    L. Székelyhidi

Authors
  1. J. M. Almira
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  2. L. Székelyhidi
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Correspondence to J. M. Almira.

Additional information

The research was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. NK-81402.

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Almira, J.M., Székelyhidi, L. Characterization of Classes of Polynomial Functions. Mediterr. J. Math. 13, 301–307 (2016). https://doi.org/10.1007/s00009-014-0463-5

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  • DOI: https://doi.org/10.1007/s00009-014-0463-5

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