Geodesic
Differentiation with Respect to Random Binary Nets and Uniqueness of Multiple Trigonometric Series
Matematičeskie zametki, Tome 88 (2010) no. 1, pp. 78-96 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that the main uniqueness properties of a multiple trigonometric series are equivalent to similar properties of the corresponding series with respect to a multiple Haar system with variable coefficients. Uniqueness theorems for multiple trigonometric series are proved under different conditions on the coefficients and on the derivative with respect to random binary nets of the sums of the series resulting from their single integration.
Keywords: differentiation with respect to random binary nets, multiple trigonometric series, multiple Haar system, Fourier series
Mots-clés : Lebesgue measure. 
@article{MZM_2010_88_1_a6,
     author = {A. A. Talalyan},
     title = {Differentiation with {Respect} to {Random} {Binary} {Nets} and {Uniqueness} of {Multiple} {Trigonometric} {Series}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {78--96},
     year = {2010},
     volume = {88},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a6/}
}
TY  - JOUR
AU  - A. A. Talalyan
TI  - Differentiation with Respect to Random Binary Nets and Uniqueness of Multiple Trigonometric Series
JO  - Matematičeskie zametki
PY  - 2010
SP  - 78
EP  - 96
VL  - 88
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a6/
LA  - ru
ID  - MZM_2010_88_1_a6
ER  - 
%0 Journal Article
%A A. A. Talalyan
%T Differentiation with Respect to Random Binary Nets and Uniqueness of Multiple Trigonometric Series
%J Matematičeskie zametki
%D 2010
%P 78-96
%V 88
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a6/
%G ru
%F MZM_2010_88_1_a6
A. A. Talalyan. Differentiation with Respect to Random Binary Nets and Uniqueness of Multiple Trigonometric Series. Matematičeskie zametki, Tome 88 (2010) no. 1, pp. 78-96. http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a6/

[1] A. Zigmund, Trigonometricheskie ryady, v. 1, Mir, 1965 | MR | Zbl

[2] V. G. Chelidze, Nekotorye metody summirovaniya dvoinykh ryadov i dvoinykh integralov, Izd-vo Tbilissk. un-ta, Tbilisi, 1977 | MR | Zbl

[3] A. A. Talalyan, “O edinstvennosti kratnykh trigonometricheskikh ryadov i garmonicheskikh funktsii”, Dokl. RAN, 294:4 (1987), 796–799 | MR | Zbl

[4] V. A. Skvortsov, A. A. Talalyan, “Nekotorye voprosy edinstvennosti kratnykh ryadov po sisteme Khaara i trigonometricheskoi sisteme”, Matem. zametki, 46:2 (1989), 104–113 | MR | Zbl

[5] A. A. Talalyan, “O edinstvennosti i integriruemosti kratnykh trigonometricheskikh ryadov”, Matem. zametki, 86:5 (2009), 761–775 | MR | Zbl

[6] J. Bourgain, “Spherical summation and uniqueness of multiple trigonometric series”, Internat. Math. Res. Notices, 1996, no. 3, 93–107 | DOI | MR | Zbl

[7] J. M. Ash, G. Wang, “Some spherical uniqueness theorems for multiple trigonometric series”, Ann. of Math. (2), 151:1 (2000), 1–33 | DOI | MR | Zbl

[8] B. Connes, “Sur les coefficients des séries trigonométriques convergentes sphériquement”, C. R. Acad. Sci. Paris Sér. A, 283:4 (1976), 159–161 | MR | Zbl