Approximative Compactness and Acting Points

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI:10.1134/S1061920825600527

A.R. Alimov, N.A. Ilyasov

引用次数: 0

Abstract

It is shown that, in many problems of geometric approximation theory related to min- and max-approximative compactness, it suffices to consider not the entire unit sphere, but rather its only part consisting of acting points (for a given set \(M\)) — these being the points of the unit sphere such that \(M\) can be touched by an “analog” of such a point on some homothetic copy of the unit ball. CLUR- and VDS-point for a set are introduced, and their relations to points of min- and max- approximative (norm, weak) compactness are studied. In terms of these points, balayage theorems for problems of min- and max- approximative (norm, weak) compactness of suns and max-suns are obtained.

DOI 10.1134/S1061920825600527

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近似紧致性与作用点

结果表明，在与最小逼近紧性和最大逼近紧性有关的几何逼近理论的许多问题中，不应考虑整个单位球，而应考虑由作用点组成的唯一部分（对于给定集合\(M\)）——这些点是单位球上的点，使得\(M\)可以被单位球的某个同质副本上的这样一个点的“类似物”所触及。引入了集合的clr -和vds点，研究了它们与最小和最大逼近（范数，弱）紧性点的关系。在这些点的基础上，得到了太阳和最大太阳的最小和最大逼近（范数，弱）紧性问题的balayage定理。Doi 10.1134/ s1061920825600527

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.