Inequivalence of Wavelet Systems in $L₁(ℝ^d)$ and $BV(ℝ^d)$

Paweł Bechler

Inequivalence of Wavelet Systems in

L ₁ (ℝ^{d})

and

B V (ℝ^{d})

Paweł Bechler

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005), p. 25-37 / Harvested from The Polish Digital Mathematics Library

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Résumé

Theorems stating sufficient conditions for the inequivalence of the d-variate Haar wavelet system and another wavelet system in the spaces $L ₁ (ℝ^{d})$ and $B V (ℝ^{d})$ 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 $L ₁ (ℝ^{d})$ is also shown.

Publié le : 2005-01-01

Zbl 1112.42016

EUDML-ID : urn:eudml:doc:280749

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     author = {Pawe\l\ Bechler},
     title = {Inequivalence of Wavelet Systems in $L1(R^d)$ and $BV(R^d)$
            },
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {53},
     year = {2005},
     pages = {25-37},
     zbl = {1112.42016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-4}
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Paweł Bechler. Inequivalence of Wavelet Systems in $L₁(ℝ^d)$ and $BV(ℝ^d)$
            . Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 25-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-4/