Geodesic
Haar series on compact zero-dimensional abelian group
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 1, pp. 14-19 
S. F. Lukomskii. Haar series on compact zero-dimensional abelian group. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 1, pp. 14-19. http://geodesic.mathdoc.fr/item/ISU_2009_9_1_a2/
@article{ISU_2009_9_1_a2,
     author = {S. F. Lukomskii},
     title = {Haar series on compact zero-dimensional abelian group},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {14--19},
     year = {2009},
     volume = {9},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2009_9_1_a2/}
}
TY  - JOUR
AU  - S. F. Lukomskii
TI  - Haar series on compact zero-dimensional abelian group
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2009
SP  - 14
EP  - 19
VL  - 9
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ISU_2009_9_1_a2/
LA  - ru
ID  - ISU_2009_9_1_a2
ER  - 
%0 Journal Article
%A S. F. Lukomskii
%T Haar series on compact zero-dimensional abelian group
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2009
%P 14-19
%V 9
%N 1
%U http://geodesic.mathdoc.fr/item/ISU_2009_9_1_a2/
%G ru
%F ISU_2009_9_1_a2

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

In this article we construct a Haar system on compact zero-dimensional abelian group as shifts and powers of some characters system. We find conditions under which a Fourier–Haar series of continuous function converge uniformly. We find groups for which Haar functions generated from one function by the operation of shifts, powers and dilations.

[1] Kashin S. B., Saakyan A. A., Ortogonalnye ryady, AFTs, M., 1999 | Zbl

[2] Kozyrev S. V., “Teoriya vspleskov kak $p$-adicheskii spektralnyi analiz”, Izv. RAN. Ser. mat., 66:2 (2002), 149–158 | DOI | MR | Zbl

[3] Shelkovich V., Skopina M., $p$-Adic Haar multiresolution analysis and pseudo-differential operators, 2008, arXiv: 0705.2294 | MR

[4] Khrennikov A. Yu., Shelkovich V. M., Skopina M., $p$-Adic refinable function and MRA-based wavelets, 2008, arXiv: 0711.2820 | MR

[5] Farkov Yu. A., “Ortogonalnye veivlety s kompaktnymi nositelyami na lokalno kompaktnykh abelevykh gruppakh”, Izv. RAN. Ser. mat., 69:3 (2005), 193–220 | DOI | MR | Zbl

[6] Farkov Yu. A., “Ortogonalnye veivlety na pryamykh proizvedeniyakh tsiklicheskikh grupp”, Mat. zametki, 82:6 (2007), 934–952 | DOI | MR | Zbl

[7] Benedetto J. J., Benedetto R. L., “A wavelet theory for local fields and related groups”, The J. of Geometric Analysis, 14:3 (2004), 423–456 | DOI | MR | Zbl

[8] Agaev G. N., Vilenkin N. Ya., Dzhafarli G. M., Rubinshtein A. I., Multiplikativnye sistemy funktsii i garmonicheskii analiz na nul-mernykh gruppakh, ELM, Baku, 1981 | MR

[9] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, M., 1982 | MR | Zbl