Geodesic
Uniqueness Questions for Some Classes of Haar Series
Matematičeskie zametki, Tome 75 (2004) no. 3, pp. 392-404 
M. G. Plotnikov. Uniqueness Questions for Some Classes of Haar Series. Matematičeskie zametki, Tome 75 (2004) no. 3, pp. 392-404. http://geodesic.mathdoc.fr/item/MZM_2004_75_3_a6/
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     author = {M. G. Plotnikov},
     title = {Uniqueness {Questions} for {Some} {Classes} of {Haar} {Series}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_3_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Sets of relative uniqueness for Haar series are studied. Whole classes of conditions on the behavior of a Haar series, including the Arutyunyan–Talalyan condition, are considered. New numerical characteristic of perfect sets are introduced. They are used to obtain necessary conditions and sufficient conditions for a given set to be a set of relative uniqueness under certain assumptions. Thereby, the 1967 results of G. M. Mushegyan are generalized. Moreover, for $0, the existence of perfect $\operatorname{U}$-sets with the $\operatorname{G}(p)$-conditions introduced by W. Wade in 1981 is proved and a method for constructing such sets is given.

[1] Petrovskaya M. B., “Nekotorye teoremy edinstvennosti dlya ryadov po sisteme Khaara”, Vestn. Mosk. un-ta. Ser. 1. Matem., 1964, no. 5, 15–28 | Zbl

[2] Arutyunyan F. G., Talalyan A. A., “O edinstvennosti ryadov po sistemam Khaara i Uolsha”, Izv. AN SSSR. Ser. matem., 28 (1964), 1391–1408 | MR | Zbl

[3] Skvortsov V. A., “Teorema tipa Kantora dlya sistemy Khaara”, Vestn. Mosk. un-ta. Ser. 1. Matem., 1964, no. 5, 15–28

[4] McLaughlin J., Price J. J., “Comparision of Haar series with gaps with trigonometric series”, Pasif. J. Math., 28:3 (1969), 623–627 | MR | Zbl

[5] Mushegyan G. M., “O mnozhestvakh edinstvennosti dlya sistemy Khaara”, Izv. AN ArmSSR. Ser. matem., 2:6 (1967), 350–361 | MR | Zbl

[6] Skvortsov V. A., “Differentsirovanie otnositelno setei i ryady Khaara”, Matem. zametki, 4:1 (1968), 33–40 | MR | Zbl

[7] Wade W. R., “Sets of uniqueness for Haar series”, Acta Math. Academiae Scientiarum Hungaricae, 30:3–4 (1977), 265–281 | DOI | MR