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
Cet article a éte moissonné depuis 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.
@article{ISU_2007_7_1_a7,
author = {P. A. Terekhin},
title = {Basis conditions for systems of translates and dilates of functions in $L_p$-spaces},
journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
pages = {39--44},
year = {2007},
volume = {7},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a7/}
}
TY - JOUR AU - P. A. Terekhin TI - Basis conditions for systems of translates and dilates of functions in $L_p$-spaces JO - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics PY - 2007 SP - 39 EP - 44 VL - 7 IS - 1 UR - http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a7/ LA - ru ID - ISU_2007_7_1_a7 ER -
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/
[1] Chanturiya Z. A., “O bazisakh prostranstva nepreryvnykh funktsii”, Mat. sbornik, 88:4 (1972), 589–608 | Zbl
[2] Saburova T. N., “O bazisakh v $C[0,1]$ tipa Fabera–Shaudera”, Teoriya funktsii i priblizhenii, Tr. tretei Sarat. zimnei shkoly (Saratov, 1986), Ch. 3, Saratov, 1988, 44–46
[3] Terekhin P. A., “Bazisy Rissa, porozhdennye szhatiyami i sdvigami funktsii na otrezke”, Mat. zametki, 72:4 (2002), 547–560 | DOI | MR | Zbl