1. bookVolume 16 (2021): Issue 1 (June 2021)
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30 Dec 2013
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access type Open Access

On the Classification of Solutions of Quantum Functional Equations with Cyclic and Semi-Cyclic Supports

Published Online: 30 Oct 2021
Page range: 1 - 40
Received: 03 Aug 2020
Accepted: 26 Dec 2020
Journal Details
License
Format
Journal
First Published
30 Dec 2013
Publication timeframe
1 time per year
Languages
English
Abstract

In this paper, we classify all solutions with cyclic and semi-cyclic semigroup supports of the functional equations arising from multiplication of quantum integers with fields of coefficients of characteristic zero. This also solves completely the classification problem proposed by Melvyn Nathanson and Yang Wang concerning the solutions, with semigroup supports which are not prime subsemigroups of ℕ, to these functional equations for the case of rational field of coefficients. As a consequence, we obtain some results for other problems raised by Nathanson concerning maximal solutions and extension of supports of solutions to these functional equations in the case where the semigroup supports are not prime subsemigroups of ℕ.

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