Hilbert generalizations $b$-Bessel systems
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 3, pp. 3-10.

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The notion of $b$-Bessel systems that generalizes the known classic notion of Bessel systems is introduced, the criteria of Bessel property of the systems are established. Some properties of the space of coefficients corresponding to the $b$-basis generalizing the classic notion of Schauder basis are studied.
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M. I. Ismailov. Hilbert generalizations $b$-Bessel systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 3, pp. 3-10. http://geodesic.mathdoc.fr/item/ISU_2011_11_3_a0/

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