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Izvestiya: Mathematics, 2016, Volume 80, Issue 3, Pages 481–488
DOI: https://doi.org/10.1070/IM8346 (Mi im8346) 		 
Quasi-greedy property of subsystems of the multivariate Haar system

S. L. Gogyan

Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan
English version PDF (227 kB) Russian version article
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DOI: https://doi.org/10.1070/IM8346
Abstract: We describe all sets of dyadic cubes $\Delta=\{\Delta_k\}$ for which a subsystem of the multivariate Haar system $\{h_i\colon\operatorname{supp}({h_i})\in\Delta\}$ is quasi-greedy in $L_1(0,1)^d$. We prove that the greedy algorithm provides a good rate of convergence for those subsystems.
Keywords: greedy algorithm, quasi-greedy basis, Haar system in $L^1$, subsystem of the Haar system.
Received: 29.01.2015
Bibliographic databases:
Document Type: Article
UDC: 517.51
MSC: Primary 41A65; Secondary 42A10
Language: English
Original paper language: Russian
Citation: S. L. Gogyan, “Quasi-greedy property of subsystems of the multivariate Haar system”, Izv. Math., 80:3 (2016), 481–488
Citation in format AMSBIB
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\pages 481--488
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