Approximative Properties of Multivariate Exponential Sums

IF 1.9 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI:10.1134/S1061920825602046

A.R. Alimov, I.G. Tsar’kov

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Abstract

Approximative properties of multivariate exponential sums are studied in \(C(D)\), \(D\) is a nonempty convex compact body in \(\mathbb{R}^d\). Properties of existence, uniqueness, solarity, and monotone path-connectedness are considered. Several classes of multivariate exponential sums are shown to be proximinal in \(C(D)\). The set \(\mathbf{E}_n^+\) of multivariate exponential sums with nonnegative coefficients is shown to be a monotone path-connected strict sun in \(C(Q)\), but not a uniqueness set. We also obtain some negative results on the lack of solarity and monotone path-connectedness for \(E_n\) (the set of extended univariate exponential sums) in \(C[a,b]\). In particular, we show that \(E_n\), \(n\ge 2\), is not monotone path-connected and is not Menger-connected in \(C[a,b]\). It is also proved that \(E_n\), \(n> 2\), is not a sun in \(C[a,b]\).

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多元指数和的近似性质

研究了\(C(D)\)中多元指数和的近似性质，\(\mathbb{R}^d\)中\(D\)是一个非空凸紧体。考虑了存在性、唯一性、唯一性和单调路径连通性的性质。在\(C(D)\)中证明了几类多元指数和是近邻的。在\(C(Q)\)中证明了多元非负系数指数和集\(\mathbf{E}_n^+\)是一个单调路径连通的严格集，但不是一个唯一性集。我们也得到了关于\(C[a,b]\)中\(E_n\)（扩展单变量指数和集）缺乏solarity和单调路径连通性的一些否定结果。特别地，我们证明了\(E_n\), \(n\ge 2\)，在\(C[a,b]\)中不是单调路径连通的，也不是menger连通的。也证明了\(E_n\)、\(n> 2\)不是\(C[a,b]\)中的太阳。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.