Abstract
In this paper, we main 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 ({\text{S}}_{\text{0}}^{{\text{ - 1}}}(\Delta), {\text{S}}_{\text{1}}^{\text{0}}(\Delta), {\text{S}}_{\text{3}}^{\text{1}} (\Delta) and {\text{S}}_{\text{4}}^{\text{2}} (\Delta), respectively) by modifying the definition of initial functions and taking Fourier transform on B-splines defined by convolution.