指数半多项式及其在半群上的表征

IF 0.9 3区 数学 Q2 MATHEMATICS
Bruce Ebanks
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引用次数: 0

摘要

半群上的指数半多项式是群上指数多项式的自然概括。我们证明,群上指数多项式的几个标准性质也适用于半群上的指数半多项式。主要结果是,对于属于某一类的拓扑交换单元 S,当且仅当 C(S) 中的函数包含在有限维平移不变线性子空间中时,它就是指数半多项式。我们还证明,关于交换半群上多项式的一些标准结果实际上在所有半群上都有效。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exponential semi-polynomials and their characterization on semigroups

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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来源期刊
Aequationes Mathematicae
Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.70
自引率
12.50%
发文量
62
审稿时长
>12 weeks
期刊介绍: aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.
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