Inequivalence of Wavelet Systems in $L_1({\Bbb R}^d)$ and ${\rm BV}({\Bbb R}^d)$

Paweł Bechler

doi:10.4064/ba53-1-4

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Inequivalence of Wavelet Systems in

L_{1} (R^{d})

and

B V (R^{d})

Paweł Bechler ¹

¹ Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 P.O. Box 21 00-956 Warszawa, Poland

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

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

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

L_{1} (R^{d})

is also shown.

DOI : 10.4064/ba53-1-4

Mots-clés : 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

¹ Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 P.O. Box 21 00-956 Warszawa, Poland

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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. https://geodesic-test.mathdoc.fr/articles/10.4064/ba53-1-4/

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