Geodesic
On the completeness of a~system of functions on a~segment
Matematičeskie zametki, Tome 4 (1968) no. 5, pp. 557-568.

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The question is considered of the completeness of the systems of functions $\{x^{\lambda_n}[1+\varepsilon_n]\}$, where $\varepsilon_n(x)$ are small, in the spaces $C$ and $L_p$ on the segment $[0,a]$. 
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     author = {L. A. Leont'eva},
     title = {On the completeness of a~system of functions on a~segment},
     journal = {Matemati\v{c}eskie zametki},
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     year = {1968},
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L. A. Leont'eva. On the completeness of a~system of functions on a~segment. Matematičeskie zametki, Tome 4 (1968) no. 5, pp. 557-568. http://geodesic.mathdoc.fr/item/MZM_1968_4_5_a8/