Wavelets on a Bounded Interval 论文

摘要

The aim of this paper is to present two different approaches to the study of multiresolution analysis and wavelets on a bounded interval. Recently, Meyer obtained orthonormal wavelets on a bounded interval by restricting Daubechies’ scaling functions and wavelets to [0, 1] and applying the Gram-Schmidt procedure to orthonormalize the restrictions. Our own approach — presented in the second part of the paper — is based on the semi-orthogonal Chui-Wang spline-wavelets. In this case we no longer have orthogonality in one scale, but there are explicit formulae for these wavelets.