Interpolatory subdivision schemes induced by box splines

This paper is devoted to a study of interpolatory refinable functions. If a refinable function phi on R-S is continuous and fundamental, i.e., phi(0) = 1 and phi(alpha)= 0 for alpha is an element of Z(S)\{0}, then its corresp onding mask b satisfies b(0) = 1 and b(2 alpha) = 0 for all alpha is an ele ment of Z(S)\{0}. Such a refinement mask is called an interpolatory mask. W e establish the existence and uniqueness of interpolatory masks which are i nduced by masks of box splines whose shifts are linearly independent. (C) 2 000 Academic Press.