Geodesic
Perturbation of the trigonometric system in~$L_1(0,\pi)$
Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 429-436

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In this paper, we study a special perturbation of the function system obtained from the Fejér kernel. It is shown how this relates to the stability of bases and complete systems as well to the stability of the trigonometric system. An approximation algorithm in systems resulting from a perturbation of the original system is given.
Keywords: trigonometric system, perturbation of the trigonometric system, the space $L_1(0,\pi)$, complete and minimal system, stability of the trigonometric system.
Mots-clés : Fejér kernel 
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     author = {V. I. Filippov},
     title = {Perturbation of the trigonometric system in~$L_1(0,\pi)$},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a12/}
}
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V. I. Filippov. Perturbation of the trigonometric system in~$L_1(0,\pi)$. Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 429-436. http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a12/