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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
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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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2016, Volume 80, Issue 3, Pages 23–30
DOI: https://doi.org/10.4213/im8346
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. RAN. Ser. Mat., 80:3 (2016), 23–30; Izv. Math., 80:3 (2016), 481–488
Citation in format AMSBIB
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:59
    English version PDF:11
    References:58
    First page:23
     
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