Geodesic
A system of functions
Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 855-860 Cet article a éte moissonné depuis la source Math-Net.Ru

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A system of functions $$ f_k(x)=\sum_{i=1}^r\alpha_i\varphi_i(x)^k+b_i\overline\varphi_i(x)^k,\quad k=1,2,\dots $$ is considered on the interval $[0,l]$. Under certain conditions on the $\varphi_i(x)$, it is proved that the system $1\cup\{f_k(x)\}_{k=1}^\infty$ is complete in the space $L_p(0,l)$. In the case $r=1$ it is proved, under certain additional assumptions, that the system $\{f_k(x)\}_{k=0}^\infty$ is minimal. 
@article{MZM_1975_18_6_a6,
     author = {A. A. Shkalikov},
     title = {A~system of functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {855--860},
     year = {1975},
     volume = {18},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a6/}
}
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A. A. Shkalikov. A system of functions. Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 855-860. http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a6/