Convergence of regularized greedy approximations
- 作者: Svetlov I.P.1
-
隶属关系:
- Lomonosov Moscow State University
- 期: 卷 89, 编号 2 (2025)
- 页面: 114-127
- 栏目: Articles
- URL: https://bakhtiniada.ru/1607-0046/article/view/303949
- DOI: https://doi.org/10.4213/im9608
- ID: 303949
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详细
We consider a new version of a greedy algorithm in biorthogonal systems in separable Banach spaces.We consider approximations of an element $f$ via $m$-term greedy sum, which isconstructed from the expansion by choosing the first$m$ greatest in absolute value coefficients.It is known that the greedy algorithm does not always converge to the original element.We prove a theorem showing that the new version of a greedy algorithm(called the regularized greedy algorithm) always converges to the original element in Efimov–Stechkin spaces. We also construct examples that show the significance of the conditions of the main theorem.
作者简介
Iurii Svetlov
Lomonosov Moscow State University
编辑信件的主要联系方式.
Email: yuri.svetlov@math.msu.ru
without scientific degree, no status
参考
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