Necessary Conditions for the Existence of Multidimensional Refinable Functions

CABRELLI, CARLOS A.; HEIL, CHRISTOPHER; MOLTER, URSULA M.

Wavelet Applications in Image and Signal Processing VIII

CRC Press

Lugar: San Diego; Año: 2000; p. 153 - 164

In this paper we outline the main ideas behind the recent proof of theauthors that if a multivariate, multi-function refinement equation withan arbitrary dilation matrix has a continuous, compactly supported solutionwhich has independent lattice translates, then the joint spectral radiusof certain matrices restricted to an appropriate subspace is strictlyless than one.