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Subsets of rectifiable curves in Banach spaces I: Sharp exponents in traveling salesman theorems

IF 0.6 Q3 MATHEMATICS
Illinois Journal of Mathematics Pub Date : 2020-02-27 DOI:10.1215/00192082-10592363
Matthew Badger, Sean McCurdy
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引用次数: 5

Abstract

The Analyst's Traveling Salesman Problem is to find a characterization of subsets of rectifiable curves in a metric space. This problem was introduced and solved in the plane by Jones in 1990 and subsequently solved in higher-dimensional Euclidean spaces by Okikiolu in 1992 and in the infinite-dimensional Hilbert space $\ell_2$ by Schul in 2007. In this paper, we establish sharp extensions of Schul's necessary and sufficient conditions for a bounded set $E\subset\ell_p$ to be contained in a rectifiable curve from $p=2$ to $1
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Banach空间I中可整流曲线的子集:旅行推销员定理中的锐指数
分析员的旅行推销员问题是找到度量空间中可直曲线子集的特征。Jones于1990年在平面中引入并求解了这个问题，随后Okikiolu于1992年在高维欧几里得空间中求解了这个，Schul于2007年在无限维Hilbert空间$\ell_2$中求解了它。在本文中，我们建立了Schul关于有界集$E\subet\ell_p$包含在从$p=2$到$1
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
Illinois Journal of Mathematics
Illinois Journal of Mathematics 数学-数学
CiteScore
0.90
自引率
0.00%
发文量
18
期刊介绍： IJM strives to publish high quality research papers in all areas of mainstream mathematics that are of interest to a substantial number of its readers. IJM is published by Duke University Press on behalf of the Department of Mathematics at the University of Illinois at Urbana-Champaign.
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