论文标题
贪婪的基础，用于序列有间隙的序列
Greedy-like bases for sequences with gaps
论文作者
论文摘要
在[25]中，T。Oikhberg介绍并研究了带有空白的序列的贪婪和弱贪婪算法的变体，重点关注$ \ Mathbf n $ -t $ -t $ t $ -quasi-quasi-quasi-quasi-greedy属性。在这个基础的基础上，我们目前的工作旨在进一步研究这些算法和基础，同时引入两个主要目的的新想法。首先，我们的目标是证明，对于$ \ Mathbf n $，带有有界商的差距，$ \ mathbf n $ - $ t $ -quasi-greedy bases是准蛋白质基础。这种概括将先前在[7]中建立的结果扩展到Markushevich基础的背景，还可以完成[25]中问题的答案。第二个目标是将贪婪算法的某些近似属性扩展到序列的上下文，并研究是否存在这种新扩展与通常的收敛之间的关系。
In [25], T. Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the $\mathbf n$-$t$-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. Firstly, we aim to prove that for $\mathbf n$ with bounded quotient gaps, $\mathbf n$-$t$-quasi-greedy bases are quasi-greedy bases. This generalization extends the result previously established in [7] to the context of Markushevich bases and, also, completes the answer to a question from [25]. 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.
