Geodesic
Wavelets on~topological groups
Izvestiya. Mathematics , Tome 44 (1995) no. 3, pp. 515-529

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Constructions are proposed for wavelets on locally compact abelian groups. A Parseval–Plancherel identity and reconstruction formulas are proved, and a number of examples are given. Wavelets in the usual sense are a special case of the wavelets considered in this paper. 
@article{IM2_1995_44_3_a3,
     author = {T. P. Lukashenko},
     title = {Wavelets on~topological groups},
     journal = {Izvestiya. Mathematics },
     pages = {515--529},
     publisher = {mathdoc},
     volume = {44},
     number = {3},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_44_3_a3/}
}
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T. P. Lukashenko. Wavelets on~topological groups. Izvestiya. Mathematics , Tome 44 (1995) no. 3, pp. 515-529. http://geodesic.mathdoc.fr/item/IM2_1995_44_3_a3/