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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. RAN. Ser. Mat., 2020 Volume 84, Issue 2, Pages 43–59 (Mi im8891)

This article is cited in 5 papers

Greedy approximation by arbitrary set

P. A. Borodin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We define various algorithms for greedy approximations by elements of an arbitrary set $M$ in a Banach space. We study the convergence of these algorithms in a Hilbert space under various geometric conditions on $M$. As a consequence, we obtain sufficient conditions for the additive semigroup generated by $M$ to be dense.

Keywords: greedy approximation, Hilbert space, density of a semigroup.

UDC: 517.982.256

MSC: 41A65

Received: 31.12.2018
Revised: 08.06.2019

DOI: 10.4213/im8891


 English version:
Izvestiya: Mathematics, 2020, 84:2, 246–261

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© Steklov Math. Inst. of RAS, 2025