Geodesic
Coefficients with respect to orthogonal-like decomposition systems
Sbornik. Mathematics, Tome 188 (1997) no. 12, pp. 1783-1798 
T. P. Lukashenko. Coefficients with respect to orthogonal-like decomposition systems. Sbornik. Mathematics, Tome 188 (1997) no. 12, pp. 1783-1798. http://geodesic.mathdoc.fr/item/SM_1997_188_12_a3/
@article{SM_1997_188_12_a3,
     author = {T. P. Lukashenko},
     title = {Coefficients with respect to orthogonal-like decomposition systems},
     journal = {Sbornik. Mathematics},
     pages = {1783--1798},
     year = {1997},
     volume = {188},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_12_a3/}
}
TY  - JOUR
AU  - T. P. Lukashenko
TI  - Coefficients with respect to orthogonal-like decomposition systems
JO  - Sbornik. Mathematics
PY  - 1997
SP  - 1783
EP  - 1798
VL  - 188
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_1997_188_12_a3/
LA  - en
ID  - SM_1997_188_12_a3
ER  - 
%0 Journal Article
%A T. P. Lukashenko
%T Coefficients with respect to orthogonal-like decomposition systems
%J Sbornik. Mathematics
%D 1997
%P 1783-1798
%V 188
%N 12
%U http://geodesic.mathdoc.fr/item/SM_1997_188_12_a3/
%G en
%F SM_1997_188_12_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

Properties of orthogonal-like decomposition systems are analyzed. It is shown in § 1 that such systems have most properties of orthogonal systems; the properties of the coefficients of the corresponding expansions are studied. A criterion enabling one to determine whether an orthogonal-like system is an orthogonal projection of an orthogonal system is established in § 2. In § 3 it is shown that Parseval's equality holds for a system satisfying certain natural conditions if and only if this is an orthogonal-like decomposition system.

[1] Danford N., Shvarts Dzh. T., Lineinye operatory. Obshaya teoriya, T. 1, IL, M., 1962

[2] Iosida K., Funktsionalnyi analiz, Mir, M., 1987 | MR

[3] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989 | MR

[4] “Besselya neravenstvo”, Matematicheskaya entsiklopediya, T. 1, Sovetskaya entsiklopediya, M., 1977, 459 | Zbl

[5] Lukashenko T. P., “O sistemakh razlozheniya, podobnykh ortogonalnym”, Mezhdunarodnaya konf. po teor. priblizh. funkts., posv. pamyati prof. P. P. Korovkina, Tezisy dokl. (Kaluga, 26–29 iyunya 1996 g.), Izd-vo TGU, Tver, 1996, 135–136

[6] Gabor D., “Theory of communication”, J. Inst. Elec. Eng. (London), 93 (3) (1946), 429–457

[7] Gasquet C., Witomski P., Analyse de Fourier et applications, Masson, Paris, 1990

[8] Lukashenko T. P., “Vspleski na topologicheskikh gruppakh”, Dokl. AN, 332:1 (1993), 15–17 | Zbl

[9] Lukashenko T. P., “Vspleski na topologicheskikh gruppakh”, Izv. RAN. Ser. matem., 58:3 (1994), 88–102 | Zbl

[10] Lukashenko T. P., “Sistemy razlozheniya na prostranstvakh s meroi”, Izv. RAN. Ser. matem., 60:1 (1996), 165–174 | MR | Zbl

[11] Grossmann A., Morlet J., “Decomposition of Hardy functions into square integrable wavelets of constant shape”, SIAM J. Math. Anal., 15 (1984), 723–736 | DOI | MR | Zbl