ON MULTIRESOLUTION ANALYSIS OF MULTIPLICITY-D

In this paper we study some basic properties of multiresolution analys is of multiplicity d in several variables and discuss some examples re lated to the spaces of cardinal splines with respect to the unidiagona l or the crisscross partition of the plane. Furthermore, in analogy wi th [8], we show that if the scaling functions are compactly supported, then it is possible to find compactly supported mother wavelets psi(1 ), l = 1,..., 2(n) d - d, in such a way that the family {2(jn/2)psi(1) (2(j) x - v)} is a semi-orthogonal basis of L-2 (R-n).