Geodesic
Haar System on the Product of Groups of~$p$-Adic Integers
Matematičeskie zametki, Tome 90 (2011) no. 4, pp. 541-557

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We present an algorithm for constructing dilation operators on the product of groups of $p$-adic integers and construct a system of Haar functions which is obtained from a single function by using the operations of contraction, translation, and raising to a power. In the two-dimensional case, we describe all the Haar bases.
Keywords: system of Haar functions, the group of $p$-adic integers, wavelet basis, Haar basis, compact group, Rademacher function, dilation operator, cyclic subgroup, coset.
Mots-clés : quotient group 
@article{MZM_2011_90_4_a5,
     author = {S. F. Lukomskii},
     title = {Haar {System} on the {Product} of {Groups} of~$p${-Adic} {Integers}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {541--557},
     publisher = {mathdoc},
     volume = {90},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a5/}
}
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S. F. Lukomskii. Haar System on the Product of Groups of~$p$-Adic Integers. Matematičeskie zametki, Tome 90 (2011) no. 4, pp. 541-557. http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a5/