Multivariate box spline wavelets in higher-dimensional Sobolev spaces

Abstract

Abstract We construct wavelets and derive a density condition of MRA in a higher-dimensional Sobolev space. We give necessary and sufficient conditions for orthonormality of wavelets in Hs(Rd) $H^{s}(\mathbb {R}^{d})$. We construct nonseparable orthonormal wavelets in a higher-dimensional Sobolev space by using multivariate box spline.

Keywords

• Wavelets
• Box Splines
• Multiresolution analysis
• Sobolev space