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Systems of dilated functions: Completeness, minimality, basisness
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 94-97 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
     year = {2017},
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     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/

[1] J. H. Neuwirth, J. Ginsberg, D. J. Newman, J. Funct. Anal., 5 (1970), 194–203 | DOI | MR | Zbl

[2] H. Hedenmalm, P. Lindqvist, K. Seip, Duke Math. J., 86:1 (1997), 1–37 | DOI | MR | Zbl

[3] N. Nikolski, Ann. Inst. Fourier (Grenoble), 62:5 (2012), 1601–1626 | DOI | MR | Zbl

[4] B. Mityagin, arXiv: 1512.07276

[5] K. S. Kazaryan, P. I. Lizorkin, Trudy MIAN, 187, 1989, 98–115

[6] K. Moen, J. Math. Anal. Appl., 371:1 (2010), 266–281 | DOI | MR | Zbl