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Mathematics of Computation

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Hybrid spline frames


Authors: Say Song Goh, Tim N. T. Goodman and S. L. Lee
Journal: Math. Comp. 78 (2009), 1537-1551
MSC (2000): Primary 65D07, 41A15; Secondary 42C40, 42C30
DOI: https://doi.org/10.1090/S0025-5718-09-02192-9
Published electronically: January 21, 2009
MathSciNet review: 2501062
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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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Additional Information

Say Song Goh
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Email: matgohss@nus.edu.sg

Tim N. T. Goodman
Affiliation: Department of Mathematics, The University of Dundee, Dundee DD1 4HN, Scotland, United Kingdom
Email: tgoodman@maths.dundee.ac.uk

S. L. Lee
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Email: matleesl@nus.edu.sg

DOI: https://doi.org/10.1090/S0025-5718-09-02192-9
Keywords: Uniform splines, geometric splines, hybrid splines, multiresolution, tight frames
Received by editor(s): September 26, 2006
Received by editor(s) in revised form: March 15, 2008
Published electronically: January 21, 2009
Additional Notes: This research was partially supported by the Wavelets and Information Processing Programme of the Centre for Wavelets, Approximation and Information Processing, National University of Singapore, under a grant from DSTA
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.