Geodesic
Lower Bounds for $n$-Term Approximations of Plane Convex Sets and Related Topics
Matematičeskie zametki, Tome 72 (2002) no. 4, pp. 509-515

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In this paper, we establish lower bounds for $n$-term approximations in the metric of$L^2(I^2)$ of characteristic functions of plane convex subsets of the square $I^2$ with respect to arbitrary orthogonal systems. It is shown that, as $n\to \infty $, these bounds cannot decrease more rapidly than $1/n$. 
@article{MZM_2002_72_4_a3,
     author = {B. S. Kashin},
     title = {Lower {Bounds} for $n${-Term} {Approximations} of {Plane} {Convex} {Sets} and {Related} {Topics}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {509--515},
     publisher = {mathdoc},
     volume = {72},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_4_a3/}
}
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B. S. Kashin. Lower Bounds for $n$-Term Approximations of Plane Convex Sets and Related Topics. Matematičeskie zametki, Tome 72 (2002) no. 4, pp. 509-515. http://geodesic.mathdoc.fr/item/MZM_2002_72_4_a3/