Hybrid spline frames
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- by Say Song Goh, Tim N. T. Goodman and S. L. Lee PDF
- Math. Comp. 78 (2009), 1537-1551 Request permission
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.References
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Additional Information
- Say Song Goh
- Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
- MR Author ID: 331333
- 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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2501062