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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Compactly supported tight affine spline frames in $L_2(\mathbb R^d)$
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by Amos Ron and Zuowei Shen PDF
Math. Comp. 67 (1998), 191-207 Request permission

Abstract:

The theory of fiberization is applied to yield compactly supported tight affine frames (wavelets) in $L_{2}(\mathbb {R}^{d})$ from box splines. The wavelets obtained are smooth piecewise-polynomials on a simple mesh; furthermore, they exhibit a wealth of symmetries, and have a relatively small support. The number of “mother wavelets”, however, increases with the increase of the required smoothness. Two bivariate constructions, of potential practical value, are highlighted. In both, the wavelets are derived from four-direction mesh box splines that are refinable with respect to the dilation matrix $\begin {pmatrix}1&1\ 1&-1\end {pmatrix}$.
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Additional Information
  • Amos Ron
  • Affiliation: Computer Science Department, University of Wisconsin-Madison, 1210 West Dayton Street, Madison, Wisconsin 53706
  • Email: amos@cs.wisc.edu
  • Zuowei Shen
  • Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
  • MR Author ID: 292105
  • Email: matzuows@leonis.nus.sg
  • Received by editor(s): February 19, 1996
  • Received by editor(s) in revised form: August 21, 1996
  • Additional Notes: This work was supported by the National Science Foundation under Grants DMS-9102857, DMS-9224748, and by the U.S. Army Research Office under Contracts DAAL03-G-90-0090, DAAH04-95-1-0089.
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 191-207
  • MSC (1991): Primary 42C15, 41A15, 41A63; Secondary 42C30
  • DOI: https://doi.org/10.1090/S0025-5718-98-00898-9
  • MathSciNet review: 1433269