2017
Том 69
№ 9

All Issues

Estimates for wavelet coefficients on some classes of functions

Babenko V. F., Spector S. A.

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Abstract

Let $ψ_m^D$ be orthogonal Daubechies wavelets that have $m$ zero moments and let $$W^k_{2, p} = \left\{f \in L_2(\mathbb{R}): ||(i \omega)^k \widehat{f}(\omega)||_p \leq 1\right\}, \;k \in \mathbb{N},$$. We prove that $$\lim_{m\rightarrow\infty}\sup\left\{\frac{|\psi^D_m, f|}{||(\psi^D_m)^{\wedge}||_q}: f \in W^k_{2, p} \right\} = \frac{\frac{(2\pi)^{1/q-1/2}}{\pi^k}\left(\frac{1 - 2^{1-pk}}{pk -1}\right)^{1/p}}{(2\pi)^{1/q-1/2}}.$$

English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 12, pp 1791-1799.

Citation Example: Babenko V. F., Spector S. A. Estimates for wavelet coefficients on some classes of functions // Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1594–1600.

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