Construction of a class of multivariate compactly supported wavelet bases for L 2(a"e d )

In this paper, for a given dxd expansive matrixM with |detM| = 2, we investigate the compactly supported M-wavelets for L-2(R-d). Starting with a pair of compactly supported refinable functions phi and (phi) over tilde satisfying a mild condition, we obtain an explicit construction of a compactly supported wavelet psi such that {2(j/2)psi(M-j . -k): j is an element of Z, k is an element of Z(d)} forms a Riesz basis for L-2(R-d). The (anti-) symmetry of such psi is studied, and some examples are also provided.