Geodesic
Quasi-greedy property of subsystems of the multivariate Haar system
Izvestiya. Mathematics , Tome 80 (2016) no. 3, pp. 481-488

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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. 
@article{IM2_2016_80_3_a1,
     author = {S. L. Gogyan},
     title = {Quasi-greedy property of subsystems of the multivariate {Haar} system},
     journal = {Izvestiya. Mathematics },
     pages = {481--488},
     publisher = {mathdoc},
     volume = {80},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2016_80_3_a1/}
}
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S. L. Gogyan. Quasi-greedy property of subsystems of the multivariate Haar system. Izvestiya. Mathematics , Tome 80 (2016) no. 3, pp. 481-488. http://geodesic.mathdoc.fr/item/IM2_2016_80_3_a1/