A FAMILY OF NONSEPARABLE SMOOTH COMPACTLY SUPPORTED WAVELETS

We construct smooth nonseparable compactly supported refinable functions that generate multiresolution analyses on L2(ℝd), d > 1. Using these refinable functions we construct smooth nonseparable compactly supported orthonormal wavelet systems. These systems are nonseparable, in the sense that none of its constituent functions can be expressed as the product of two functions defined on lower dimensions. Both the refinable functions and the wavelets can be made as smooth as desired. Estimates for the supports of these scaling functions and wavelets, are given.