Necessary conditions for the existence of multivariate multiscaling functions

Carlos A. Cabrelli; Christopher E. Heil; Ursula M. Molter

doi:10.1117/12.408625

4 December 2000 Necessary conditions for the existence of multivariate multiscaling functions

Carlos A. Cabrelli, Christopher E. Heil, Ursula M. Molter

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Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408625
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

In this paper we outline the main ideas behind the recent proof of the authors that if a multivariate, multi-function refinement equation with an arbitrary dilation matrix has a continuous, compactly supported solution which has independent lattice translates, then the joint spectral radius of certain matrices restricted to an appropriate subspace is strictly less than one.

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Carlos A. Cabrelli, Christopher E. Heil, and Ursula M. Molter "Necessary conditions for the existence of multivariate multiscaling functions", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408625

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