Geodesic
Haar series on compact zero-dimensional abelian group
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 1, pp. 14-19

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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. 
@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},
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     publisher = {mathdoc},
     volume = {9},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/ISU_2009_9_1_a2/}
}
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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/