Spline wavelets in periodic Sobolev spaces and application to high order collocation methods

in Revista de la Union Matematica Argentina (2003), 44(1), 53-74

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 ... [more ▼]

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. [less ▲]

A walk in the the theory of wavelets from L^2(R) to H^s(R).

in Rendiconti del circolo Matematico Di Palermo (2) Suppl (1998), 52(1), 239-252

A general functional characterization of the microlocal singularities

in Journal of Mathematical Sciences, The University of Tokyo (1995), 2(1), 155-164