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Spline wavelets on the interval with homogeneous boundary conditions

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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.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada, T6G 2G1

    Rong-Qing Jia

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  1. Rong-Qing Jia
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Correspondence to Rong-Qing Jia.

Additional information

Communicated by Tim Goodman.

Supported in part by NSERC Canada under Grant OGP 121336.

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Jia, RQ. Spline wavelets on the interval with homogeneous boundary conditions. Adv Comput Math 30, 177–200 (2009). https://doi.org/10.1007/s10444-008-9064-9

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  • DOI: https://doi.org/10.1007/s10444-008-9064-9

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