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Low-Pass Filters and Scaling Functions for Multivariable Wavelets

Published online by Cambridge University Press:  20 November 2018

Eva Curry*
Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5 e-mail:
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We show that a characterization of scaling functions for multiresolution analyses given by Hernández and Weiss and that a characterization of low-pass filters given by Gundy both hold for multivariable multiresolution analyses.

Research Article
Copyright © Canadian Mathematical Society 2008


[2] Curry, E., Radix Representations, self-affine tiles, and multivariable wavelet. Proc. Amer.Math. Soc. 134(2006), no. 8, 2411–2418.Google Scholar
[3] Belock, J. and Dobric, V., Random variable dilation equation and multidimensional prescale functions. Trans. Amer.Math. Soc. 353(2001), no. 12, 4779–4800.Google Scholar
[4] Dobrić, V., Gundy, R., and Hitczenko, P., Characterizations of orthonormal scale functions: A probabilistic approach J. Geom. Anal. 10(2000), no. 3, 417–434.Google Scholar
[5] Gröchenig, K. and Madych, W. R., Multiresolution analysis, Haar bases, and self-similar tilings of Rn. IEEE Trans. Inform. Theory. 38(1992), no. 2, 556–568.Google Scholar
[6] Gundy, R., Low-pass filters, martingales, and multiresolution analyses. Appl. Comput. Harmon. Anal. 9(2000), no. 2, 204–219.Google Scholar
[7] He, X.-G. and Lau, K.-S., Characterization of tile digit sets with prime determinants. Appl. Comput. Harmon. Anal. 16(2004), no. 3, 159–173.Google Scholar
[8] Hernández, E. and Weiss, G., A First Course on Wavelets. CRC Press, Boca Raton, FL, 1996.Google Scholar
[9] Lagarias, J. C. and Wang, Y., Self-Affine tiles in R n. Adv. Math. 121(1996), no. 1, 21–49.Google Scholar
[10] Lagarias, J. C. and Wang, Y., Integral self-affine tiles in Rn. II. Lattice tilings. J. Fourier Anal. Appl. 3(1997), no. 1, 83–102.Google Scholar
[11] Lagarias, J. C. and Wang, Y., Haar bases for L2(Rn) and algebraic number theory. J. Number Theory 57(1996), no. 1, 181–197.Google Scholar
[12] Lagarias, J. C. and Wang, Y., Corrigendum/Addendum: Haar Bases for L2(Rn) and Algebraic Number Theory, J. Number Theory 76(1999), no. 1, 330336.Google Scholar
[13] Wojtaszczyk, P., A Mathematical Introduction to Wavelets. London Mathematical Society Student Texts 37, Cambridge University Press, Cambridge, 1997.Google Scholar