Wavelet expansions on the Cantor group
Yu. A. Farkov · Mathematical Notes · 2014
Wavelet expansions in L p -spaces on the locally compact Cantor group G are studied. An order-sharp estimate of the wavelet approximation of an arbitrary function f ∈ L p (G) for 1 ≤ p < ∞ in terms of the modulus of continuity of this function is obtained, and a Jackson-Bernstein type theorem on approximation by wavelets of functions from the class Lip(p)(α; G) is proved.