Estimates for wavelet coefficients on some classes of functions

  • V. F. Babenko
  • S. A. Spector

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 $$\lim_{m\rightarrow\infty}\sup\left\{\frac{|\psi^D_m, f|}{||(\psi^D_m)^{\wedge}||_q}: f \in W^k_{2, p} \right\} = \frac{\frac{(2\pi)^{1/q-1/2}}{\pi^k}\left(\frac{1 - 2^{1-pk}}{pk -1}\right)^{1/p}}{(2\pi)^{1/q-1/2}}.$$
Published
25.12.2007
How to Cite
Babenko, V. F., and S. A. Spector. “Estimates for Wavelet Coefficients on Some Classes of Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 12, Dec. 2007, pp. 1594–1600, https://umj.imath.kiev.ua/index.php/umj/article/view/3415.
Section
Research articles