Spline wavelets on the interval with homogeneous boundary conditions

In this paper we investigate spline wavelets on the interval with homo-geneous boundary conditions. Starting with a pair of families of B-splines on the unit interval, we give a general method to explicitly construct wavelets satisfying the desired homogeneous boundary conditions. On the basis of a new development of multiresolution analysis, we show that these wavelets form Riesz bases of certain Sobolev spaces. The wavelet bases investigated in this paper are suitable for numerical solutions of ordinary and partial differential equations. Key words and phrases. Spline wavelets, wavelets on the interval, slant matrices, multiresolution analysis, Riesz bases, Sobolev spaces