Geodesic
On the rate of approach to zero of the coefficients of null series in the Haar and Walsh systems
Izvestiya. Mathematics, Tome 11 (1977) no. 3, pp. 665-676 
V. A. Skvortsov. On the rate of approach to zero of the coefficients of null series in the Haar and Walsh systems. Izvestiya. Mathematics, Tome 11 (1977) no. 3, pp. 665-676. http://geodesic.mathdoc.fr/item/IM2_1977_11_3_a9/
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     author = {V. A. Skvortsov},
     title = {On the rate of approach to zero of the coefficients of null series in the {Haar} and {Walsh} systems},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The existence of null series in the Haar system with coefficients approaching zero at any prescribed rate admissible for such series is proved, and a class of null series in the Walsh system with coefficients tending to zero sufficiently rapidly is also constructed. It is proved that the series of squares of coefficients of a null series in the Walsh system may diverge arbitrarily slowly. Bibliography: 6 titles.

[1] Bari N. K., Trigonometricheskie ryady, GIFML, M., 1961 | MR

[2] Ivashev-Musatov O. S., “O koeffitsientakh trigonometricheskikh nul-ryadov”, Izv. AN SSSR. Ser. matem., 21 (1957), 559–578 | MR | Zbl

[3] Petrovskaya M. B., “O nul-ryadakh po sisteme Khaara i mnozhestvakh edinstvennosti”, Izv. AN SSSR. Ser. matem., 28 (1964), 773–798

[4] Arutyunyan F. G., “O ryadakh po sisteme Khaara”, Dokl. AN Arm. SSR, 42:3 (1966), 134–140 | MR | Zbl

[5] Ulyanov P. L., “O ryadakh po sisteme Khaara s monotonnymi koeffitsientami”, Izv. AN SSSR. Ser. matem., 28 (1964), 925–950

[6] Skvortsov V. A., “Primer ryada Uolsha so vsyudu skhodyascheisya k nulyu podposledovatelnostyu chastichnykh summ”, Matem. sb., 97(139):4(8) (1975), 517–539 | MR | Zbl