Geodesic
Wavelet Expansions on the Cantor Group
Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 926-938

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The wavelet expansions in $L^p$-spaces on a locally compact Cantor group $G$ are studied. An order-sharp estimate of the wavelet approximation of an arbitrary function $f\in L^p(G)$ for $1\leqslant p\infty$, in terms of the modulus of continuity of this function is obtained, and a Jackson–Bernstein type theorem on the approximation by wavelets of functions from the class $\operatorname{Lip}^{(p)}(\alpha;G)$ is proved.
Keywords: wavelet expansion, Cantor group, $L^p$-space, Jackson–Bernstein type theorem, the class $\operatorname{Lip}^{(p)}(\alpha;G)$, modulus of continuity, Walsh polynomial
Mots-clés : Fourier transform. 
@article{MZM_2014_96_6_a12,
     author = {Yu. A. Farkov},
     title = {Wavelet {Expansions} on the {Cantor} {Group}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {926--938},
     publisher = {mathdoc},
     volume = {96},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a12/}
}
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Yu. A. Farkov. Wavelet Expansions on the Cantor Group. Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 926-938. http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a12/