Wavelet Expansions on the Cantor Group

Yu. A. Farkov

Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 926-938.

Résumé

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.

Détail

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.

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