Reference : Non Stationary Multiresolution Analysis
Scientific congresses and symposiums : Poster
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/91838
Non Stationary Multiresolution Analysis
English
Simons, Laurent mailto [Université de Liège - ULg > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes >]
13-Sep-2010
No
National
PhD-Day
13 septembre 2010
The Belgian Mathematical Society
Brussels
Belgium
[en] Wavelets ; Multiresolution analysis
[en] An orthonormal basis of wavelets of $L^2(\R)$ is an orthonormal basis of $L^2(\R)$ of type
\[
\psi_{j,k}=2^{j/2}\psi(2^j\cdot-k),\quad j,k\in\Z.
\]
A classical method to obtain such bases consists in constructing a multiresolution analysis. When the mother wavelet $\psi$ depends on the scale (i.e. the index $j$), a non stationary version of multiresolution analysis is then used. It is for example the case in the general context of Sobolev spaces. We generalize different characterizations in the standard theory of wavelets to the case of multi-scales wavelets and non stationary multiresolution analyses.
http://hdl.handle.net/2268/91838

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