J Austral Math Soc Ser B 37 pp474--489, 1996.

Wavelet transform of the dilation equation

Carlos A. Cabrelli and Ursula M. Molter

(Received 15 November 1993; revised 10 October 1994)

Abstract

In this article we study the dilation equation f (x) = ĺh ch  f (2x - h) in L 2(R) using a wavelet approach. We see that the structure of Multiresolution Analysis adapts very well to the study of scaling functions. The equation is reduced to an equation in a subspace of L 2(R) of much lower resolution. This simpler equation is then "wavelet transformed" to obtain a discrete dilation equation. In particular we study the case of compactly supported solutions and we see that conditions for the existence of solutions are given by convergence of infinite products of matrices. These matrices are of the type obtained by Daubechies, and, when the analyzing wavelet is the Haar wavelet, they are exactly the same.

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Authors

Carlos A. Cabrelli
Ursula M. Molter
Dept de Matemática, Universidad de Buenos Aires, Pabellón I, 1428 Capital Federal, Argentina.

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Last Modified: Mon Dec 10 13:43:33 2001

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