caa a22 4500 475741420 CHVBK 20180406123500.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1007/BF02675794 doi (NATIONALLICENCE)springer-10.1007/BF02675794 Lukashenko T. M. V. Lomonosov Moscow State University, USSR aut Analogs of the Kolmogorov-Seliverstov-Plessner theorem for nonorthogonal function systems [Elektronische Daten] [T. Lukashenko] For arbitrary function systems, the growth of partial sums is estimated depending on the growth of the corresponding Lebesgue functions. We prove analogs of the Kolmogorov-Seliverstov-Plessner convergence theorem for trigonometric series and the Kaczmarz convergence theorem for orthogonal series for arbitrary (nonorthogonal) function systems as well as for orthogonal-like and generalized orthogonal-like systems. Kluwer Academic/Plenum Publishers, 2000 nonorthogonal expansions nationallicence convergence nationallicence Parseval-Plancherel identity nationallicence Lebesgue function nationallicence Kolmogorov-Seliverstov-Plessner theorem nationallicence Kaczmarz theorem nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/1(2000-01-01), 69-80 0001-4346 67:1<69 2000 67 11006 https://doi.org/10.1007/BF02675794 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02675794 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lukashenko T. M. V. Lomonosov Moscow State University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/1(2000-01-01), 69-80 0001-4346 67:1<69 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer