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arXiv · 1708.09767

Estimation of wavelet coefficients on some classes of functions

Vladislav Babenko·Susanna Spektor
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Abstract

Let $Ψ_m^D$ be orthogonal Daubechies wavelets that have m zero moments and let $$ W_{2,p}^k=\{f \in L_2(R):\|(I ω)^k\hat f(ω)\|_p\leq 1\}, \, k \in N. $$ We prove that $$ \lim_{m \to \infty}\, \sup\left\{\frac{|(Ψ_m^D)|}{\|(\hat Ψ_m^D)\|_q}: f \in W_{2, p'}^k\right\}=\frac{\frac{(2π)^{1/p-1/2}}{π^k}\left(\frac{1-2^{1-pk}}{pk-1}\right)^{1/p}}{(2π)^{1/q-1/2}}. $$

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Vladislav Babenko, Susanna Spektor. 2017-08-31. Estimation of wavelet coefficients on some classes of functions. https://arxiv.org/abs/1708.09767

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