Geodesic
Approximation in $L^p(\mathbb R^d)$, $0$, by linear combinations of the characteristic functions of balls
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 37, Tome 366 (2009), pp. 5-12

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We prove that the translates of the characteristic function of a ball span $L^p(\mathbb R^d)$ provided $0$ and $d\ge2$. Similar approximation problems are considered for some other functions. Bibl. – 5 titles. 
@article{ZNSL_2009_366_a0,
     author = {A. B. Aleksandrov},
     title = {Approximation in $L^p(\mathbb R^d)$, $0<p<1$, by linear combinations of the characteristic functions of balls},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--12},
     publisher = {mathdoc},
     volume = {366},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_366_a0/}
}
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A. B. Aleksandrov. Approximation in $L^p(\mathbb R^d)$, $0