论贪心型碱的若干特征

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2022-12-01 DOI:10.1016/j.exmath.2022.06.003

Pablo M. Berná , Hùng Việt Chu

{"title":"论贪心型碱的若干特征","authors":"Pablo M. Berná , Hùng Việt Chu","doi":"10.1016/j.exmath.2022.06.003","DOIUrl":null,"url":null,"abstract":"<div><p><span>In 1999, S. V. Konyagin and V. N. Temlyakov introduced the so-called Thresholding </span>Greedy Algorithm<span>. Since then, there have been many interesting and useful characterizations of greedy-type bases in Banach spaces. In this article, we study and extend several characterizations of greedy and almost greedy bases in the literature. Along the way, we give various examples to complement our main results. Furthermore, we propose a new version of the so-called Weak Thresholding Greedy Algorithm (WTGA) and show that the convergence of this new algorithm is equivalent to the convergence of the WTGA.</span></p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"40 4","pages":"Pages 1135-1158"},"PeriodicalIF":0.8000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"On some characterizations of greedy-type bases\",\"authors\":\"Pablo M. Berná , Hùng Việt Chu\",\"doi\":\"10.1016/j.exmath.2022.06.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>In 1999, S. V. Konyagin and V. N. Temlyakov introduced the so-called Thresholding </span>Greedy Algorithm<span>. Since then, there have been many interesting and useful characterizations of greedy-type bases in Banach spaces. In this article, we study and extend several characterizations of greedy and almost greedy bases in the literature. Along the way, we give various examples to complement our main results. Furthermore, we propose a new version of the so-called Weak Thresholding Greedy Algorithm (WTGA) and show that the convergence of this new algorithm is equivalent to the convergence of the WTGA.</span></p></div>\",\"PeriodicalId\":50458,\"journal\":{\"name\":\"Expositiones Mathematicae\",\"volume\":\"40 4\",\"pages\":\"Pages 1135-1158\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Expositiones Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0723086922000482\",\"RegionNum\":4,\"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":"Expositiones Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0723086922000482","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 5

摘要

1999年，S. V. Konyagin和V. N. Temlyakov引入了所谓的阈值贪婪算法。此后，对Banach空间中的贪心型基有了许多有趣而有用的刻画。本文研究并推广了文献中关于贪心基和几乎贪心基的几个刻画。在此过程中，我们给出了各种例子来补充我们的主要结果。在此基础上，提出了一种新的弱阈值贪婪算法(WTGA)，并证明了该算法的收敛性等同于WTGA算法的收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On some characterizations of greedy-type bases

In 1999, S. V. Konyagin and V. N. Temlyakov introduced the so-called Thresholding Greedy Algorithm. Since then, there have been many interesting and useful characterizations of greedy-type bases in Banach spaces. In this article, we study and extend several characterizations of greedy and almost greedy bases in the literature. Along the way, we give various examples to complement our main results. Furthermore, we propose a new version of the so-called Weak Thresholding Greedy Algorithm (WTGA) and show that the convergence of this new algorithm is equivalent to the convergence of the WTGA.

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

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

期刊介绍： Our aim is to publish papers of interest to a wide mathematical audience. Our main interest is in expository articles that make high-level research results more widely accessible. In general, material submitted should be at least at the graduate level.Main articles must be written in such a way that a graduate-level research student interested in the topic of the paper can read them profitably. When the topic is quite specialized, or the main focus is a narrow research result, the paper is probably not appropriate for this journal. Most original research articles are not suitable for this journal, unless they have particularly broad appeal.Mathematical notes can be more focused than main articles. These should not simply be short research articles, but should address a mathematical question with reasonably broad appeal. Elementary solutions of elementary problems are typically not appropriate. Neither are overly technical papers, which should best be submitted to a specialized research journal.Clarity of exposition, accuracy of details and the relevance and interest of the subject matter will be the decisive factors in our acceptance of an article for publication. Submitted papers are subject to a quick overview before entering into a more detailed review process. All published papers have been refereed.