Advances in Computational Mathematics

, Volume 30, Issue 2, pp 177–200

Spline wavelets on the interval with homogeneous boundary conditions

Article

Abstract

In this paper we investigate spline wavelets on the interval with homogeneous 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.

Keywords

Spline wavelets Wavelets on the interval Slant matrices Multiresolution analysis Riesz bases Sobolev spaces 

Mathematics Subject Classifications (2000)

42C40 41A15 46B15 

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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada

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