同心圆上离散符号测度的绿色能量

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2023-01-01 DOI:10.4213/im9343e

V. Dubinin

{"title":"同心圆上离散符号测度的绿色能量","authors":"V. Dubinin","doi":"10.4213/im9343e","DOIUrl":null,"url":null,"abstract":"We show that the difference between the Green energy of a discrete signed measure relative to a circular annulus concentrated at some points on concentric circles and the energy of the signed measure at symmetric points is non-decreasing during the expansion of the annulus. As a corollary, generalizations of the classical Pólya-Schur inequality for complex numbers are obtained. Some open problems are formulated.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Green energy of discrete signed measure on concentric circles\",\"authors\":\"V. Dubinin\",\"doi\":\"10.4213/im9343e\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the difference between the Green energy of a discrete signed measure relative to a circular annulus concentrated at some points on concentric circles and the energy of the signed measure at symmetric points is non-decreasing during the expansion of the annulus. As a corollary, generalizations of the classical Pólya-Schur inequality for complex numbers are obtained. Some open problems are formulated.\",\"PeriodicalId\":54910,\"journal\":{\"name\":\"Izvestiya Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4213/im9343e\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4213/im9343e","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了在环空的扩展过程中，集中在同心圆上某些点上的离散有符号测量的相对于环空的绿色能量与对称点上的有符号测量的能量之差不减小。作为推论，得到了classicalPólya-Schur不等式对复数的推广。一些开放问题被公式化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Green energy of discrete signed measure on concentric circles

We show that the difference between the Green energy of a discrete signed measure relative to a circular annulus concentrated at some points on concentric circles and the energy of the signed measure at symmetric points is non-decreasing during the expansion of the annulus. As a corollary, generalizations of the classical Pólya-Schur inequality for complex numbers are obtained. Some open problems are formulated.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.