Geodesic
Bases in the spaces $C$ and $L_p$
Matematičeskie zametki, Tome 10 (1971) no. 6, pp. 635-640

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In this paper it is proved that for any numbers $A$ and $B$, $0$, there exists a basis in the space $C$ consisting of functions $\varphi_k(x)$, $k=1,2,\dots$, whose graphs lie in the strip $0\leqslant x\leqslant1$, $A\leqslant y\leqslant B$. It is shown that for the space $L_p$, $p>1$, there is no analogous “basis in a strip” theorem. 
@article{MZM_1971_10_6_a4,
     author = {M. A. Meletidi},
     title = {Bases in the spaces $C$ and $L_p$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {635--640},
     publisher = {mathdoc},
     volume = {10},
     number = {6},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a4/}
}
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M. A. Meletidi. Bases in the spaces $C$ and $L_p$. Matematičeskie zametki, Tome 10 (1971) no. 6, pp. 635-640. http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a4/