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Matematicheskie Zametki, 2006, Volume 80, Issue 3, Pages 429–436
DOI: https://doi.org/10.4213/mzm2829 (Mi mzm2829) 		 
Perturbation of the trigonometric system in $L_1(0,\pi)$

V. I. Filippov

Saratov State Socio-Economic University
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DOI: https://doi.org/10.4213/mzm2829
Abstract: 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, Fejér kernel, the space $L_1(0,\pi)$, complete and minimal system, stability of the trigonometric system.
Received: 23.04.2003
Revised: 15.03.2006
English version:
Mathematical Notes, 2006, Volume 80, Issue 3, Pages 410–416
DOI: https://doi.org/10.1007/s11006-006-0154-z
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: V. I. Filippov, “Perturbation of the trigonometric system in $L_1(0,\pi)$”, Mat. Zametki, 80:3 (2006), 429–436; Math. Notes, 80:3 (2006), 410–416
Citation in format AMSBIB
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