Greedy-like bases for sequences with gaps

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-21 DOI:10.1007/s43037-024-00324-2

Miguel Berasategui, Pablo M. Berná

引用次数: 0

Abstract

In 2018, Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the \({{\textbf {n}}}\)-t-quasi-greedy property that is based on them. Building upon this foundation, our current work aims to further investigate these algorithms and bases while introducing new ideas for two primary purposes. First, we aim to prove that for \({{\textbf {n}}}\) with bounded quotient gaps, \({{\textbf {n}}}\)-t-quasi-greedy bases are quasi-greedy bases. This generalization extends a previous result to the context of Markushevich bases and, also, completes the answer to a question by Oikhberg. The second objective is to extend certain approximation properties of the greedy algorithm to the context of sequences with gaps and study if there is a relationship between this new extension and the usual convergence.

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有间隙序列的类贪心碱基

2018 年，Oikhberg 介绍并研究了有间隙序列的贪婪算法和弱贪婪算法的变体，重点研究了基于它们的 \({{\textbf {n}}}\)-t- 准贪婪性质。在此基础上，我们当前的工作旨在进一步研究这些算法和基础，同时为两个主要目的引入新思路。首先，我们旨在证明对于有界商隙的\({{\textbf {n}}\) 来说，\({{textbf {n}}\)-t- 准贪基是准贪基。这一概括将之前的一个结果扩展到了马库舍维奇基的范畴，同时也完成了对奥伊赫伯格所提问题的回答。第二个目标是将贪心算法的某些近似性质扩展到有缺口的序列中，并研究这一新扩展与通常收敛之间是否存在关系。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.