On the Classification of Solutions of Quantum Functional Equations with Cyclic and Semi-Cyclic Supports-Reference-Cited by-同舟云学术

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

Published:2021-06-01 Issue:1 Volume:16 Page:1-40
ISSN:2309-5377
Container-title:Uniform distribution theory
language:en
Short-container-title:

Author:

Nguyen Lan¹

Affiliation:

1. Department of Mathematics , The University of Wisconsin-Parkside , Kenosha , Wisconsin, USA

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/udt-2021-0001

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