Reference : Spline wavelets in periodic Sobolev spaces and application to high order collocation met...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/28690
Spline wavelets in periodic Sobolev spaces and application to high order collocation methods
English
Bastin, Françoise mailto [Université de Liège - ULg > Département de mathématique > Analyse, analyse fonctionnelle, ondelettes >]
Boigelot, Christine [> >]
Laubin, Pascal [> >]
2003
Revista de la Union Matematica Argentina
44
1
53-74
Yes
International
0041-6932
[en] Sobolev spaces ; splines ; wavelets ; collocation methods
[en] In this paper, we present a particular family of spline wavelets constructed from the Chui-Wang Riesz basis of $L^2(\mathbb{R})$. The construction is explicit, allowing the study of specific functional properties and rather easy handling in numerical computations. This family constitutes a Riesz hierarchical basis in periodic Sobolev spaces. We also present a necessary and sufficient condition of strong ellipticity for pseudodifferential operators obtained with respect to these splines. It uses a new expression for the numerical symbol of the boundary integral operators. This expression allows us to use efficiently collocation methods with different meshes and splines.
http://hdl.handle.net/2268/28690

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