Construction of multivariate tight frames via Kronecker products

Integer-translates of compactly supported univariate refinable functions ph i (i), such as cardinal B-splines, have been used extensively in computatio nal mathematics. Using certain appropriate direction vectors, the notion of (multivariate) box splines can be generalized to (non-tensor-product) comp actly supported multivariate refinable functions Phi from the phi (i)'s. Th e objective of this paper is to introduce a Kronecker-product approach to b uild compactly supported tight frames associated with Phi, using the two-sc ale symbols of the univariate tight frame generators associated with the ph i (i)'s. (C) 2001 Academic Press.