Geodesic
Basis conditions for systems of translates and dilates of functions in $L_p$-spaces
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 1, pp. 39-44 
P. A. Terekhin. Basis conditions for systems of translates and dilates of functions in $L_p$-spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 1, pp. 39-44. http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a family of translates and dilates of function (or in other words family of wavelets on finite interval) in Lebesgue spaces. The explicit expressions for biorthogonal family are given. The theorem of equiconvergence for biorthogonal wavelets series and Fourier–Haar series is established.

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