Hybrid spline frames

Goh, Say; Goodman, Tim; Lee, S.

doi:10.1090/S0025-5718-09-02192-9

Hybrid spline frames
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by Say Song Goh, Tim N. T. Goodman and S. L. Lee;

Math. Comp. 78 (2009), 1537-1551

DOI: https://doi.org/10.1090/S0025-5718-09-02192-9

Published electronically: January 21, 2009

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Abstract:

Using their unitary extension principle, Ron and Shen have constructed a normalized tight frame for $L^2(\mathbb {R})$ consisting of spline functions with uniform knots. This paper constructs a normalized tight frame for $L^2((0,\infty ))$ comprising spline functions with knots on a hybrid of uniform and geometric mesh. The construction is motivated by applications in adaptive approximation using spline functions on a hybrid mesh that admits a natural dyadic multiresolution approximation of $L^2((0,\infty ))$ based on dilation and translation.

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