Inequivalence of Wavelet Systems in $L₁\left({ℝ}^d\right)$ and $BV\left({ℝ}^d\right)$

Paweł Bechler. "Inequivalence of Wavelet Systems in $L₁(ℝ^d)$ and $BV(ℝ^d)$." Bulletin of the Polish Academy of Sciences. Mathematics 53.1 (2005): 25-37. <http://eudml.org/doc/280749>.

@article{PawełBechler2005,
abstract = {Theorems stating sufficient conditions for the inequivalence of the d-variate Haar wavelet system and another wavelet system in the spaces $L₁(ℝ^d)$ and $BV(ℝ^d)$ are proved. These results are used to show that the Strömberg wavelet system and the system of continuous Daubechies wavelets with minimal supports are not equivalent to the Haar system in these spaces. A theorem stating that some systems of smooth Daubechies wavelets are not equivalent to the Haar system in $L₁(ℝ^d)$ is also shown.},
author = {Paweł Bechler},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Haar system; wavelets; inequivalence},
language = {eng},
number = {1},
pages = {25-37},
title = {Inequivalence of Wavelet Systems in $L₁(ℝ^d)$ and $BV(ℝ^d)$},
url = {http://eudml.org/doc/280749},
volume = {53},
year = {2005},
}

TY - JOUR
AU - Paweł Bechler
TI - Inequivalence of Wavelet Systems in $L₁(ℝ^d)$ and $BV(ℝ^d)$
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2005
VL - 53
IS - 1
SP - 25
EP - 37
AB - Theorems stating sufficient conditions for the inequivalence of the d-variate Haar wavelet system and another wavelet system in the spaces $L₁(ℝ^d)$ and $BV(ℝ^d)$ are proved. These results are used to show that the Strömberg wavelet system and the system of continuous Daubechies wavelets with minimal supports are not equivalent to the Haar system in these spaces. A theorem stating that some systems of smooth Daubechies wavelets are not equivalent to the Haar system in $L₁(ℝ^d)$ is also shown.
LA - eng
KW - Haar system; wavelets; inequivalence
UR - http://eudml.org/doc/280749
ER -