Reference : A note about non stationary multiresolution analysis

	Document type :	Scientific congresses and symposiums : Unpublished conference
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/2268/113469

Title :	A note about non stationary multiresolution analysis
Language :	English
Author, co-author :	Simons, Laurent [Université de Liège - ULg > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes >]
Publication date :	28-Jul-2011
On invitation :	No
Audience :	International
Event name :	International Conference on Applied Harmonic Analysis and Multiscale Computing
Event date :	du 25 juillet 2011 au 31 juillet 2011
Event organizer :	Elena Braverman, Bin Han, Rong-Qing Jia, Yau Shu Wong, Ozgur Yilmaz
Event place (city) :	Edmonton
Event country :	Canada
Keywords :	[en] Wavelets ; Multiresolution Analysis ; Orthonormal Basis
Abstract :	[en] An orthonormal basis of wavelets of $L^2(\mathbb{R})$ is an orthonormal basis of $L^2(\mathbb{R})$ of type \[ \psi_{j,k}=2^{j/2}\psi(2^j\cdot-k),\quad j,k\in\mathbb{Z}. \] 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. We generalize different characterizations of orthonormal bases of wavelets to the non stationary case (as main reference for the stationary case, we used results presented in "A First Course of Wavelets" of E. Hernandez and G. Weiss).
Target :	Researchers ; Professionals
Permalink :	http://hdl.handle.net/2268/113469

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