M-band subdivision of bivariate B-splines of uniform partition in three directions

In this paper, we mainly discuss the refinability of the bivariate B-splines of uniform partition in three directions. We construct the M- band refinement equations of bivariate B-splines of uniform partition in three directions in four spaces (S/sub 0//sup -1/ (/spl Delta/), S/sub 1//sup 0/ (/spl Delta/), S/sub 3//sup 1/ (/spl Delta/) and S/sub 4//sup 2/ (/spl Delta/), respectively) by modifying the definition of initial functions and taking Fourier transform on B-splines defined by convolution.