WAVELET DECOMPOSITIONS IN L(2)(IR(2))

Let {V(k)}k=-infinity(+infinity) be a multiresolution analysis generat ed by a function phi(x) is-an-element-of L2(R2). Under this multiresol ution framework the key point for studying wavelet decompositions in L 2(R2) is to study the properties of W0 which is the orthogonal complem ent of V0 in V1:V1 = V0 + W0. In this paper the author studies the str ucture of W0 and furthermore shows that a box spline of three directio ns can generate a wavelet decomposition of L2(R2).