| Institute of Mathematics of the Polish Academy of Sciences |
| BULLETIN |
| of the |
| POLISH ACADEMY of SCIENCES |
| MATHEMATICS |
| ISSN: 0239-7269(p) 1732-8985(e) |
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Abstract:
\def\BV{{\rm BV}}\def\RR{{\sym R}}Theorems stating sufficient conditions for the inequivalence of the
$d$-variate Haar wavelet system and another wavelet
system in the spaces $L_1(\RR^d)$ and $\BV(\RR^d)$ are proved. These
results are used to show that the Str\"omberg 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 $L_1(\RR^d)$ is also shown.