Geodesic
Systems of dilated functions: Completeness, minimality, basisness
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 94-97

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The completeness, minimality, and basis property in $L^2[0,\pi]$ and $L^p[0,\pi]$, $p\neq 2$, are considered for systems of dilated functions $u_n(x)= S(nx)$, $n \in \mathbb{N}$, where $S$ is the trigonometric polynomial $S(x)=\sum_{k=0}^m a_k\sin(kx)$, $a_0 a_m \neq 0$. A series of results are presented and several unanswered questions are mentioned.
Keywords: completeness, minimality of systems of functions
Mots-clés : bases $L^p$ spaces. 
@article{FAA_2017_51_3_a7,
     author = {B. S. Mityagin},
     title = {Systems of dilated functions: {Completeness,} minimality, basisness},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {94--97},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a7/}
}
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B. S. Mityagin. Systems of dilated functions: Completeness, minimality, basisness. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 94-97. http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a7/