$\varphi$信封的实现集和泛型属性

Pub Date : 2019-06-17 DOI:10.7146/MATH.SCAND.A-110766

A. Cabot, A. Jourani, L. Thibault, D. Zagrodny

{"title":"$\\varphi$信封的实现集和泛型属性","authors":"A. Cabot, A. Jourani, L. Thibault, D. Zagrodny","doi":"10.7146/MATH.SCAND.A-110766","DOIUrl":null,"url":null,"abstract":"The attainment set of the $\\varphi$-envelope of a function at a given point is investigated. The inclusion of the attainment set of the $\\varphi$-envelope of the closed convex hull of a function into the attainment set of the function is preserved in sufficiently general settings to encompass the case $\\varphi$ being a norm in a power not less than $1$. The non-emptiness of the attainment set is guaranteed on generic subsets of a given space, in several fundamental cases.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The attainment set of the $\\\\varphi$-envelope and genericity properties\",\"authors\":\"A. Cabot, A. Jourani, L. Thibault, D. Zagrodny\",\"doi\":\"10.7146/MATH.SCAND.A-110766\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The attainment set of the $\\\\varphi$-envelope of a function at a given point is investigated. The inclusion of the attainment set of the $\\\\varphi$-envelope of the closed convex hull of a function into the attainment set of the function is preserved in sufficiently general settings to encompass the case $\\\\varphi$ being a norm in a power not less than $1$. The non-emptiness of the attainment set is guaranteed on generic subsets of a given space, in several fundamental cases.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2019-06-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7146/MATH.SCAND.A-110766\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7146/MATH.SCAND.A-110766","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

研究了函数在给定点上$\varphi$-包络的可达集。将函数的闭凸包的$\varphi$包络的可达集包含到函数的可达集中，是在足够通用的设置中保留的，以包含$\varphi$是不小于$1$幂的范数的情况。在几个基本情况下，在给定空间的泛型子集上保证了可达集的非空性。

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

The attainment set of the $\varphi$-envelope and genericity properties

The attainment set of the $\varphi$-envelope of a function at a given point is investigated. The inclusion of the attainment set of the $\varphi$-envelope of the closed convex hull of a function into the attainment set of the function is preserved in sufficiently general settings to encompass the case $\varphi$ being a norm in a power not less than $1$. The non-emptiness of the attainment set is guaranteed on generic subsets of a given space, in several fundamental cases.

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