Inequivalence of Wavelet Systems in $L_1({\Bbb R}^d)$ and ${\rm BV}({\Bbb R}^d)$
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 1, pp. 25-37
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Theorems stating sufficient conditions for the inequivalence of the
$d$-variate Haar wavelet system and another wavelet
system in the spaces $L_1(\mathbb R^d)$ and $\mathop{\rm BV}(\mathbb R^d)$ 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 $L_1(\mathbb R^d)$ is also shown.
Keywords:
theorems stating sufficient conditions inequivalence d variate haar wavelet system another wavelet system spaces mathbb mathop mathbb proved these results str mberg wavelet system system continuous daubechies wavelets minimal supports equivalent haar system these spaces theorem stating systems smooth daubechies wavelets equivalent haar system mathbb shown
Affiliations des auteurs :
Paweł Bechler 1
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title = {Inequivalence of {Wavelet} {Systems} in $L_1({\Bbb R}^d)$ and ${\rm BV}({\Bbb R}^d)$},
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Paweł Bechler. Inequivalence of Wavelet Systems in $L_1({\Bbb R}^d)$ and ${\rm BV}({\Bbb R}^d)$. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 1, pp. 25-37. doi: 10.4064/ba53-1-4
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