Geodesic
Nonlinear approximation of functions from the class $L^r$ with respect to the Vilenkin system
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2013), pp. 30-39

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In this paper we prove that for any function $f$ from the class $L^r$ on $[0,1)$ one can find a function $g$ from the same class (which differs from $f$ on a set of arbitrarily small measure) whose greedy algorithm with respect to the Vilenkin system converges to $f$.
Keywords: Vilenkin system, greedy algorithm
Mots-clés : Fourier coefficients. 
@article{IVM_2013_2_a2,
     author = {M. G. Grigoryan and S. A. Sargsyan},
     title = {Nonlinear approximation of functions from the class $L^r$ with respect to the {Vilenkin} system},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {30--39},
     publisher = {mathdoc},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_2_a2/}
}
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M. G. Grigoryan; S. A. Sargsyan. Nonlinear approximation of functions from the class $L^r$ with respect to the Vilenkin system. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2013), pp. 30-39. http://geodesic.mathdoc.fr/item/IVM_2013_2_a2/