Biorthogonal Box Spline Wavelet

Some speciic box splines are reenable functions with respect to nn expanding integer scaling matrices M satisfying M n = 2I: Therefore they can be used to deene a multiresolution analysis and a wavelet basis associated with these scaling matrices. In this paper, we construct biorthogonal wavelet bases for this special subclass of box splines. These speciic bases can also be used to derive wavelets with respect to classical dyadic scaling matrices. * The work of the rst author has been supported by Deutsche Forschungsgemeinschaft (DA360/1-1). y The second author would like to thank the Institut f ur Geometrie und Praktische Mathematik for its hospitality and support. He also acknowledges partial support by NSF grant DMS-9306430.