We consider Bessel sequences in Banach space with respect to modeling sequences space. The generalized analogues of theorems of Bari, Schur, Novikov and Czaja are established.
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.
