Geodesic
On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 37, Tome 366 (2009), pp. 67-83

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Suppose $B$ is a subset of integers that possesses certain arithmetic properties. Estimates of the best approximation of functions in the space $L_p$, $0$, by trigonometric polynomials that are constructed by the system $\{e^{ikx}\}_{k\in\mathbb Z\setminus B}$ are obtained. Bibl. – 13 titles. 
@article{ZNSL_2009_366_a4,
     author = {Yu. S. Kolomoitsev},
     title = {On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0<p<1$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--83},
     publisher = {mathdoc},
     volume = {366},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_366_a4/}
}
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Yu. S. Kolomoitsev. On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$, $0