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A characterization of generalized exponential polynomials in terms of decomposable functions

  • M. LaczkovichEmail author
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Abstract

Let G be a topological commutative semigroup with unit. We prove that a continuous function \({f\colon {G} \to \mathbb{C}}\) is a generalized exponential polynomial if and only if there is an \({n \geq 2}\) such that \({f(x_{1} + {\cdots} +x_{n})}\) is decomposable; that is, if \({f(x_{1} + {\cdots} +x_{n}) = \sum_{i=1}^{k} u_{i} \cdot v_{i}}\), where the function ui only depends on the variables belonging to a set \({\emptyset \neq E_{i} \subsetneq \{x_{1},\ldots, x_{n}\}}\), and vi only depends on the variables belonging to \({\{x_{1},\ldots,x_{n}\} \setminus E_{i} (i = 1,\ldots,k)}\).

Key words and phrases

generalized exponential polynomial decomposable function 

Mathematics Subject Classification

primary 39B52 secondary 22A20 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Eötvös Loránd UniversityBudapestHungary

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