Geodesic
Decomposition systems on spaces with a~measure
Izvestiya. Mathematics , Tome 60 (1996) no. 1, pp. 169-178

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We propose a general construction of various decomposition systems for square-integrable functions, partial instances, of which are continuous wavelet decompositions. We give an analogue of the Parseval–Plancherel identity and a reconstruction formula as well as a number of examples of decomposition systems. 
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     author = {T. P. Lukashenko},
     title = {Decomposition systems on spaces with a~measure},
     journal = {Izvestiya. Mathematics },
     pages = {169--178},
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     volume = {60},
     number = {1},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1996_60_1_a6/}
}
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T. P. Lukashenko. Decomposition systems on spaces with a~measure. Izvestiya. Mathematics , Tome 60 (1996) no. 1, pp. 169-178. http://geodesic.mathdoc.fr/item/IM2_1996_60_1_a6/