Buhmann, M.D. and Davydov, Oleg and Goodman, T.N.T. (2003) Cubic spline prewavelets on the fourdirectional mesh. Foundations of Computational Mathematics, 3 (2). pp. 113133.

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Abstract
In this paper, we design differentiable, two dimensional, piecewise polynomial cubic prewavelets of particularly small compact support. They are given in closed form, and provide stable, orthogonal decompositions of $L^2(\RR^2)$. In particular, the splines we use in our prewavelet constructions give rise to stable bases of spline spaces that contain all cubic polynomials, whereas the more familiar box spline constructions cannot reproduce all cubic polynomials, unless resorting to a box spline of higher polynomial degree.
Item type:  Article 

ID code:  36561 
Keywords:  prewavelets , cubic polynomials , spline constructions, Mathematics, Computational Theory and Mathematics, Computational Mathematics, Theoretical Computer Science, Applied Mathematics, Mathematics(all) 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Pure Administrator 
Date Deposited:  22 Dec 2011 16:05 
Last modified:  21 May 2015 14:15 
URI:  http://strathprints.strath.ac.uk/id/eprint/36561 
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