Construction of Multivariate Tight Frames via Kronecker Products

AbstractInteger-translates of compactly supported univariate refinable functions φi, such as cardinal B-splines, have been used extensively in computational mathematics. Using certain appropriate direction vectors, the notion of (multivariate) box splines can be generalized to (non-tensor-product) compactly supported multivariate refinable functions Φ from the φi's. The objective of this paper is to introduce a Kronecker-product approach to build compactly supported tight frames associated with Φ, using the two-scale symbols of the univariate tight frame generators associated with the φi's