Tight compactly supported wavelet frames of arbitrarily high smoothness
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- by Karlheinz Gröchenig and Amos Ron PDF
- Proc. Amer. Math. Soc. 126 (1998), 1101-1107 Request permission
Abstract:
Based on Ron and Shen’s new method for constructing tight wave- let frames, we show that one can construct, for any dilation matrix, and in any spatial dimension, tight wavelet frames generated by compactly supported functions with arbitrarily high smoothness.References
- Carl de Boor, Ronald A. DeVore, and Amos Ron, The structure of finitely generated shift-invariant spaces in $L_2(\textbf {R}^d)$, J. Funct. Anal. 119 (1994), no. 1, 37–78. MR 1255273, DOI 10.1006/jfan.1994.1003
- Albert Cohen and Ingrid Daubechies, Nonseparable bidimensional wavelet bases, Rev. Mat. Iberoamericana 9 (1993), no. 1, 51–137. MR 1216125, DOI 10.4171/RMI/133
- C.K. Chui, X.L. Shi and J. Stöckler, Affine frames, quasi-affine frames and their duals, CAT Report 372, Texas A&M University, College Station, TX, 77843, June 1996.
- Stephan Dahlke, Wolfgang Dahmen, and Vera Latour, Smooth refinable functions and wavelets obtained by convolution products, Appl. Comput. Harmon. Anal. 2 (1995), no. 1, 68–84. MR 1313100, DOI 10.1006/acha.1995.1006
- Ingrid Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), no. 7, 909–996. MR 951745, DOI 10.1002/cpa.3160410705
- Ingrid Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1162107, DOI 10.1137/1.9781611970104
- Karlheinz Gröchenig and Andrew Haas, Self-similar lattice tilings, J. Fourier Anal. Appl. 1 (1994), no. 2, 131–170. MR 1348740, DOI 10.1007/s00041-001-4007-6
- K. Gröchenig and W. R. Madych, Multiresolution analysis, Haar bases, and self-similar tilings of $\textbf {R}^n$, IEEE Trans. Inform. Theory 38 (1992), no. 2, 556–568. MR 1162214, DOI 10.1109/18.119723
- A. Ron and Z. Shen, Affine systems in $L_{2}(\mathbb {R}^d )$, the analysis of the analysis operator, J. Functional Anal., to appear. Ftp site: anonymous@ftp.cs.wisc.edu/Approx file affine.ps
- A. Ron and Z. Shen, Compactly supported tight affine spline frames in $L_{2}(\mathbb {R}^d )$, Math. Comp., to appear. Ftp site: anonymous@ftp.cs.wisc.edu/Approx file tight.ps
- Robert S. Strichartz, Wavelets and self-affine tilings, Constr. Approx. 9 (1993), no. 2-3, 327–346. MR 1215776, DOI 10.1007/BF01198010
Additional Information
- Karlheinz Gröchenig
- Affiliation: Department of Mathematics U-9, University of Connecticut, Storrs, Connecticut 06269-3009
- Email: groch@math.uconn.edu
- Amos Ron
- Affiliation: Department of Computer Science, University of Wisconsin-Madison, Madison, Wisconsin 53706
- Email: amos@cs.wisc.edu
- Received by editor(s): September 23, 1996
- Additional Notes: This work was supported by the National Science Foundation under Grants DMS-9224748 and DMS-9626319, and by the U.S. Army Research Office under Contract DAAH04-95-1-0089.
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1101-1107
- MSC (1991): Primary 42C15; Secondary 42C30
- DOI: https://doi.org/10.1090/S0002-9939-98-04232-4
- MathSciNet review: 1443828