Reference : Non Stationary Multiresolution Analysis

	Document type :	Scientific congresses and symposiums : Poster
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/2268/91838

Title :	Non Stationary Multiresolution Analysis
Language :	English
Author, co-author :	Simons, Laurent [Université de Liège - ULg > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes >]
Publication date :	13-Sep-2010
Audience :	National
Event name :	PhD-Day
Event date :	13 septembre 2010
Event organizer :	The Belgian Mathematical Society
Event place (city) :	Brussels
Event country :	Belgium
Keywords :	[en] Wavelets ; Multiresolution analysis
Abstract :	[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.
Permalink :	http://hdl.handle.net/2268/91838

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