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Exponential semi-polynomials and their characterization on semigroups

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Abstract

Exponential semi-polynomials on semigroups are natural generalizations of exponential polynomials on groups. We show that several of the standard properties of exponential polynomials on groups also hold for exponential semi-polynomials on semigroups. The main result is that for topological commutative monoids S belonging to a certain class, a function in C(S) is an exponential semi-polynomial if and only if it is contained in a finite dimensional translation invariant linear subspace. We also show that some standard results about polynomials on commutative semigroups are in fact valid on all semigroups.

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  1. Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS, 39762, USA

    Bruce Ebanks

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  1. Bruce Ebanks
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Correspondence to Bruce Ebanks.

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Ebanks, B. Exponential semi-polynomials and their characterization on semigroups. Aequat. Math. (2024). https://doi.org/10.1007/s00010-024-01032-w

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  • DOI: https://doi.org/10.1007/s00010-024-01032-w

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