Geodesic
Basis of the properties of weighted exponential systems with excess
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 1, pp. 14-19

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The main aim of this paper is the determination of a class of such functions for which a weighted exponential system becomes complete and minimal in appropriate space when exactly one of its terms is eliminated. It is shown that the system, obtained in this way cannot be a Schouder basis in this space. The last fact shows that Muckenhoupt-type criterion for the exponential system to be the Schauder basis in Lebesgue spaces after elimination of an element does not exist. This paper generalizes the results of the paper by E.S. Golubeva.
Keywords: system of weighted exponentials, Muckenhoupt condition. 
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     author = {A. Sh. Shukurov},
     title = {Basis of the properties of weighted exponential systems with excess},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {14--19},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2018_24_1_a1/}
}
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A. Sh. Shukurov. Basis of the properties of weighted exponential systems with excess. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 1, pp. 14-19. http://geodesic.mathdoc.fr/item/VSGU_2018_24_1_a1/