Geodesic
A property of a system of functions close to exponential functions
Matematičeskie zametki, Tome 12 (1972) no. 1, pp. 29-36 
L. A. Leont'eva. A property of a system of functions close to exponential functions. Matematičeskie zametki, Tome 12 (1972) no. 1, pp. 29-36. http://geodesic.mathdoc.fr/item/MZM_1972_12_1_a3/
@article{MZM_1972_12_1_a3,
     author = {L. A. Leont'eva},
     title = {A property of a system of functions close to exponential functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {29--36},
     year = {1972},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_1_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the system $\{f_n(x)=x^{\lambda_n}[1+\varepsilon_n(x)]\}$ in the interval $[a,b]$ ($0\leqslant a). Under certain conditions on $\lambda_n>0$ and $\varepsilon_n(x)$ such as the condition $\varlimsup\limits_{n\to\infty}\frac{\ln m_n}{\lambda_n}>0$, $m_n=||\varepsilon_n(x)||_{L_p[a,b]}$, we obtain a bound for the coefficients of the polynomial $P(x)=\sum c_nf_n(x)$ in terms of $||P(x)||_{L_p[a,b]}$. It is found that this bound is not valid without this condition (assuming the other conditions to remain the same).