Geodesic
On completeness of a~system of functions that are close to power functions
Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 400-418

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We obtain necessary and sufficient conditions for the completeness of the system $\{f_n(x)=x^{\lambda_n}[1+\varepsilon_n(x)]\}$ in $L_p[0, a]$, where $\varepsilon_n(x)\in L_p[0, a]$, $\varlimsup_{n\to\infty}\frac{\ln m_n}{\lambda_n}0$, $m_n = \|\varepsilon_n(x)\|_{L_p[0, a]}$, $n=1,2,\dots$; $1$. Bibliography: 4 titles. 
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     author = {L. A. Leont'eva},
     title = {On completeness of a~system of functions that are close to power functions},
     journal = {Sbornik. Mathematics},
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     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_13_3_a4/}
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L. A. Leont'eva. On completeness of a~system of functions that are close to power functions. Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 400-418. http://geodesic.mathdoc.fr/item/SM_1971_13_3_a4/